{"id":301,"date":"2023-07-06T15:29:16","date_gmt":"2023-07-06T15:29:16","guid":{"rendered":"https:\/\/mathority.org\/id\/matriks-involusional\/"},"modified":"2023-07-06T15:29:16","modified_gmt":"2023-07-06T15:29:16","slug":"matriks-involusional","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/matriks-involusional\/","title":{"rendered":"Matriks involusional"},"content":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu matriks involusi. Kami juga menunjukkan contoh matriks involutif berdimensi 2\u00d72, 3\u00d73, dan 4\u00d74. Dan terakhir, Anda akan menemukan rumus matriks involusional.<\/p>\n<h2 class=\"wp-block-heading\"> Apa itu matriks involusional?<\/h2>\n<p> Arti dari matriks involusional adalah sebagai berikut: <\/p>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p style=\"text-align:left\"> Pengertian <strong>matriks involutif<\/strong> : Suatu matriks persegi yang dapat dibalik yang matriks inversnya adalah matriks itu sendiri.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8711e2a47f90783a00a3bdd571df2175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{-1} = A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah matriks apa pun dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2b32875906f7ed9c10ffd1b09a6ed5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<p> mewakili kebalikannya.<\/p>\n<\/div>\n<p> Jadi jelas matriks involusional merupakan <a href=\"https:\/\/mathority.org\/id\/kapan-contoh-dan-sifat-matriks-beraturan-atau-matriks-inversi\/\">contoh matriks beraturan atau matriks tak berdegenerasi<\/a> .<\/p>\n<p> Jika anda belum mengetahui apa itu invers suatu matriks, disini anda bisa melihat cara menghitung <a href=\"https:\/\/mathority.org\/id\/matriks-terbalik\/\">invers matriks 3&#215;3<\/a> . Penting untuk mengetahui cara membalikkan matriks, namun untuk ini Anda juga perlu mengetahui cara menghitung <a href=\"https:\/\/mathority.org\/id\/contoh-adjoint-minor-matriks-dan-adjoint-komplementer-serta-latihan-penyelesaiannya\/\">adjoint suatu matriks<\/a> .<\/p>\n<p> Namun kembali ke pokok bahasan: ketika suatu matriks bersifat involutif, perkalian matriks dengan matriks itu sendiri menghasilkan matriks identitas. Lihatlah demonya:<\/p>\n<p> Setiap matriks dikalikan dengan inversnya menghasilkan matriks Identitas (atau Unit). JADI:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2326f8acf7b6701e027cafdaae59b38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot A^{-1} = I\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan karena invers dari matriks involusi adalah matriks itu sendiri:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8c3afa923ef022a2d25738eb843390b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A \\cdot A = I\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Akibatnya, matriks involusi kuadrat menghasilkan matriks identitas: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quest-ce-quune-matrice-involutive.webp\" alt=\"apa itu matriks involusional\" class=\"wp-image-3723\" width=\"68\" height=\"63\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"> Contoh matriks involusional<\/h2>\n<h3 class=\"estil_titol_H3 wp-block-heading\"> Contoh matriks involusi 2\u00d72: <\/h3>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-involutive-22152-1.webp\" alt=\"contoh matriks involutif berdimensi 2x2\" class=\"wp-image-3724\" width=\"143\" height=\"73\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Kita dapat memverifikasi bahwa ini adalah matriks involusional dengan menghitung pangkat kedua dari matriks tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-314aebadfe3da501264c0eb14e1dfc2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2=\\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] -1 &amp; -2 \\end{pmatrix} \\cdot \\begin{pmatrix} 2 &amp; 3 \\\\[1.1ex] -1 &amp; -2 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"318\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Karena matriks A kuadrat adalah matriks identitas, maka matriks A adalah matriks involusional 2\u00d72.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks involusi 3\u00d73: <\/h3>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-involutive-32153-1.webp\" alt=\"contoh matriks involutif berdimensi 3x3\" class=\"wp-image-3725\" width=\"195\" height=\"108\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Kita dapat memverifikasi bahwa ini adalah matriks involusional dengan menyelesaikan perkalian matriks itu sendiri:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-599241f00e8a89f8b55ed2ae8cb42ddb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B^2=\\begin{pmatrix} 2 &amp; 1 &amp; 1 \\\\[1.1ex] -1 &amp; 0 &amp; -1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}\\cdot \\begin{pmatrix} 2 &amp; 1 &amp; 1 \\\\[1.1ex] -1 &amp; 0 &amp; -1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"430\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Karena matriks B kuadrat adalah matriks identitas, maka matriks B adalah matriks involusional 3\u00d73.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh matriks involusi 4\u00d74:<\/h3>\n<p> Matriks Identitas (atau Unit), apa pun dimensinya, menurut definisinya adalah matriks involusional.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4278c2b46761d3b258eb9ba04c87bbf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I=\\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"143\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kita dapat memverifikasi bahwa ini adalah matriks involusional dengan menaikkan matriks menjadi 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3190f24d196c4b96a60ec06fe7180e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I^2=\\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}= \\begin{pmatrix} 1 &amp; 0 &amp; 0 &amp; 0 \\\\[1.1ex]0 &amp; 1 &amp; 0 &amp; 0\\\\[1.1ex]0 &amp; 0 &amp; 1 &amp; 0 \\\\[1.1ex]0 &amp; 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"418\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Karena matriks identitas kuadrat adalah matriks identitas, maka matriks identitas tersebut merupakan matriks involusi 4\u00d74.<\/p>\n<p> Tentu saja matriks identitas dapat berdimensi apa saja, karena matriks tersebut hanyalah sebuah matriks diagonal dengan semua angka 1 pada diagonal utama dan sisanya 0. Jadi matriks identitas akan selalu berupa matriks involusional, apapun ordenya.<\/p>\n<h2 class=\"wp-block-heading\"> Rumus matriks yang melibatkan<\/h2>\n<p> Salah satu sifat matriks involusi adalah dapat diketahui rumusnya. Namun pembuktian rumus matriks involusi orde kedua cukup membosankan, jadi langsung saja kita lihat hasilnya, itu yang penting. Jika Anda lebih tertarik dengan demonya, Anda dapat melihatnya dijelaskan langkah demi langkah di bawah di komentar.<\/p>\n<p> <strong>Rumus matriks involutif<\/strong> berdimensi 2 \u00d7 2 adalah sebagai berikut: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-matricielle-involutive.webp\" alt=\"rumus matriks bergulir\" class=\"wp-image-3726\" width=\"414\" height=\"134\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Oleh karena itu, setiap matriks yang nilai diagonal utamanya berlawanan dan determinannya -1, akan menjadi matriks involusional.<\/p>\n<p> Namun, selain matriks yang dijelaskan oleh rumus ini, harus diperhatikan bahwa <strong>matriks identitas dan kebalikannya juga merupakan matriks involusional<\/strong> berorde 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-395beb5a766a10eefa56a087e8c8d098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix} \\qquad \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"182\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks involusi<\/h2>\n<p> Matriks involusional mempunyai ciri-ciri sebagai berikut:<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Penentu matriks involusional<\/strong><\/span> selalu sama dengan -1 atau +1.<\/li>\n<\/ul>\n<ul>\n<li> Ada hubungan antara matriks involusional dan <span style=\"color:#1976d2;\"><strong>matriks idempoten<\/strong><\/span> <strong>:<\/strong> matriks\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> bersifat involusional jika dan hanya jika matriksnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37b99c07f3a3eb03d02d9448a923078e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Q= \\cfrac{1}{2} \\cdot (A+I)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"118\" style=\"vertical-align: -12px;\"><\/p>\n<p> adalah idempoten.<\/li>\n<\/ul>\n<ul>\n<li> Ya\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah dua matriks involusi <span style=\"color:#1976d2;\"><strong>komutasi<\/strong><\/span> , lalu hasil kali matriks<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89b2a721cf233a7e57685324f6648a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"AB\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> juga merupakan matriks involusional lainnya.<\/li>\n<\/ul>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Kekuatan apa pun dari matriks involusional<\/strong><\/span> akan menghasilkan matriks involusional lainnya. Secara khusus, matriks involusional yang dipangkatkan ganjil akan sama dengan matriks itu sendiri, sebaliknya jika dipangkatkan ke eksponen genap maka akan ekuivalen dengan matriks Identitas.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03f040ce22790ca420cd1614b4ee3c5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^2 = I\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-639e56b4e1e25d1a3743cd2768cf21b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^3 = A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"58\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan mempelajari apa itu matriks involusi. Kami juga menunjukkan contoh matriks involutif berdimensi 2\u00d72, 3\u00d73, dan 4\u00d74. Dan terakhir, Anda akan menemukan rumus matriks involusional. Apa itu matriks involusional? Arti dari matriks involusional adalah sebagai berikut: Pengertian matriks involutif : Suatu matriks persegi yang dapat dibalik yang matriks inversnya adalah matriks &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/matriks-involusional\/\"> <span class=\"screen-reader-text\">Matriks involusional<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[63],"tags":[],"class_list":["post-301","post","type-post","status-publish","format-standard","hentry","category-matriks-terbalik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriks involusional - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/matriks-involusional\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriks involusional - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan mempelajari apa itu matriks involusi. Kami juga menunjukkan contoh matriks involutif berdimensi 2\u00d72, 3\u00d73, dan 4\u00d74. Dan terakhir, Anda akan menemukan rumus matriks involusional. Apa itu matriks involusional? Arti dari matriks involusional adalah sebagai berikut: Pengertian matriks involutif : Suatu matriks persegi yang dapat dibalik yang matriks inversnya adalah matriks &hellip; Matriks involusional Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/matriks-involusional\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T15:29:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8711e2a47f90783a00a3bdd571df2175_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/matriks-involusional\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/matriks-involusional\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Matriks involusional\",\"datePublished\":\"2023-07-06T15:29:16+00:00\",\"dateModified\":\"2023-07-06T15:29:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/matriks-involusional\/\"},\"wordCount\":477,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Matriks terbalik\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/matriks-involusional\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/matriks-involusional\/\",\"url\":\"https:\/\/mathority.org\/id\/matriks-involusional\/\",\"name\":\"Matriks involusional - 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