{"id":2406,"date":"2012-08-18T01:41:00","date_gmt":"2012-08-18T01:41:00","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2406"},"modified":"2014-12-02T08:32:06","modified_gmt":"2014-12-02T08:32:06","slug":"finding-the-inverse-of-a-2x2-matrix","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/08\/18\/finding-the-inverse-of-a-2x2-matrix\/","title":{"rendered":"Finding the Inverse of a 2&#215;2 Matrix"},"content":{"rendered":"<p>Two matrices <strong>A<\/strong> and <strong>B<\/strong> of same order <strong>2<\/strong> are said be inverses to each other if <strong>AB=BA=I<\/strong>, where \u2018<strong>I<\/strong>\u2019 is the unit matrix of same order <strong>2<\/strong>.<\/p>\n<p>Here, A is called inverse of B and B is called inverse of A.<\/p>\n<p><strong>i.e<\/strong>. <strong>A= B<\/strong><sup><strong>&#8211;<\/strong>1<\/sup> and <strong>B= A<sup>-1<\/sup>.<\/strong><\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong><span style=\"text-decoration: underline\">Note 1:<\/span><\/strong><\/p>\n<p>From the above definition, we have<\/p>\n<p><strong>A A<sup>-1<\/sup> = A<sup>-1<\/sup> A = I<\/strong> and<\/p>\n<p><strong>B B<sup>-1<\/sup> = B<sup>-1<\/sup> B = I.<\/strong><\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/inverse-matriex1.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2408\" title=\"inverse matriex1\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/inverse-matriex1.bmp\" alt=\"\" \/><\/a><\/p>\n<p><strong><span style=\"text-decoration: underline\">Note 2:<\/span><\/strong><\/p>\n<p><strong><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/invrese-matrix21.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2410\" title=\"invrese matrix2\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/invrese-matrix21.bmp\" alt=\"\" \/><\/a><\/strong><\/p>\n<p>b)\u00a0 The inverse of a <strong>2&#215;2<\/strong> matrix exists (or <strong>A<\/strong> is invertible) only if <strong>ad-bc\u22600.<\/strong><\/p>\n<p>c)\u00a0 Inverse does not exist for a rectangular matrix.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Properties:<\/span><\/strong><\/p>\n<p>The inverse of a matrix has the following properties.<\/p>\n<p>a)\u00a0\u00a0\u00a0\u00a0 Inverse of a matrix is unique, if it exists.<\/p>\n<p>b)\u00a0\u00a0\u00a0\u00a0<strong> (AB)<sup>-1<\/sup> = B<sup>-1<\/sup> A<sup>-1<\/sup><\/strong><\/p>\n<p><a href=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/invrese-matrix3.bmp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-2411\" title=\"invrese matrix3\" src=\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/8\/2012\/07\/invrese-matrix3.bmp\" alt=\"\" \/><\/a><\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Oakland\u00a0visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-oakland-california\/\">Tutoring in Oakland.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two matrices A and B of same order 2 are said be inverses to each other if AB=BA=I, where \u2018I\u2019 is the unit matrix of same order 2. Here, A is called inverse of B and B is called inverse of A. i.e. A= B&#8211;1 and B= A-1. \u00a0 Note 1: From the above definition, [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[818,970,1081,1148],"class_list":["post-2406","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-how-do-i-use-a-matrix","tag-inverse-of-a-matrix","tag-manipulating-matrices","tag-more-about-2x2-matrices"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2406","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=2406"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2406\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}