{"id":157654,"date":"2023-09-06T14:08:40","date_gmt":"2023-09-06T08:38:40","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=157654"},"modified":"2023-09-06T14:08:41","modified_gmt":"2023-09-06T08:38:41","slug":"for-any-real-square-and-non-singular-matrix-b-the-det-b-1-is","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/for-any-real-square-and-non-singular-matrix-b-the-det-b-1-is\/","title":{"rendered":"For any real, square and non-singular matrix B , the det B-1 is"},"content":{"rendered":"\n<p>Q. For any real, square and non-singular matrix <strong>B <\/strong>, the det <strong>B<\/strong><sup>-1<\/sup> is<\/p>\n\n\n\n<p>(A) zero\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/p>\n\n\n\n<p>(B) (det <strong>B<\/strong>)<sup>-1<\/sup>\u00a0\u00a0\u00a0 <\/p>\n\n\n\n<p>(C)\u00a0-(det <strong>B<\/strong>)\u00a0\u00a0 <\/p>\n\n\n\n<p>(D) det <strong>B<\/strong><\/p>\n\n\n\n<p>Ans: (det <strong>B<\/strong>)<sup>-1<\/sup><\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>For any matrix whose inverse exists i.e. non-singular<\/p>\n\n\n\n<p>BB-1 = I <\/p>\n\n\n\n<p>|BB<sup>-1<\/sup>| = 1 <\/p>\n\n\n\n<p>|B||B<sup>-1<\/sup>| = 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"187\" height=\"40\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/Screenshot-803.png\" alt=\"\" class=\"wp-image-157666\"\/><\/figure>\n\n\n\n<p>det (B<sup>-1<\/sup>) = (det B)<sup>-1<\/sup><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. For any real, square and non-singular matrix B , the det B-1 is (A) zero\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) (det B)-1\u00a0\u00a0\u00a0 (C)\u00a0-(det B)\u00a0\u00a0 (D) det B Ans: (det B)-1 Sol: For any matrix whose inverse exists i.e. non-singular BB-1 = I |BB-1| = 1 |B||B-1| = 1 det (B-1) = (det B)-1<\/p>\n","protected":false},"author":419,"featured_media":157669,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-157654","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=157654"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157654\/revisions"}],"predecessor-version":[{"id":157670,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/157654\/revisions\/157670"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/157669"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=157654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=157654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=157654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}