{"id":17993,"date":"2026-05-02T20:23:00","date_gmt":"2026-05-02T14:23:00","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/two-by-two-matrix-test-14\/"},"modified":"2026-05-02T20:23:00","modified_gmt":"2026-05-02T14:23:00","slug":"two-by-two-matrix-test-14","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/two-by-two-matrix-test-14\/","title":{"rendered":"Two By Two Matrix Test 14"},"content":{"rendered":"<p>Decide whether the matrix [[-4, 0], [-5, 5]] is invertible.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>not enough information<\/li>\n<li>invertible<\/li>\n<li>invertible only if trace is zero<\/li>\n<li>not invertible<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705,2721],"subject":[1425],"education_level":[1896],"class_list":["post-17993","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-matrices","subject-mathematics","education_level-hsc"],"mcq_note":"To test whether a 2\u00d72 square matrix is invertible, first calculate its determinant. If the determinant is zero, the matrix has no inverse; if it is non-zero, the matrix is invertible. A square matrix is invertible exactly when its determinant is non-zero. The determinant is -4(5)-0(-5)=-20, so it is invertible. So the decision depends entirely on whether the determinant equals zero or not.","mcq_options":[{"right":"no","answer":"not enough information"},{"right":"yes","answer":"invertible"},{"right":"no","answer":"invertible only if trace is zero"},{"right":"no","answer":"not invertible"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"},{"id":2721,"title":"Matrices","slug":"matrices"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/17993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=17993"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17993"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17993"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17993"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}