Question 5 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 5 The inverse of the matrix [■(3&0&0@0&2&0@0&0&5)] is... (A) [■(0&0&3@0&2&0@5&0&0)] (B) [■(1/3&0&0@0&1/2&0@0&0&1/5)] (C) [■(−1/3&0&0@0&−1/2&0@0&0&−1/5)] (D) [■(−3&0&0@0&−2&0@0&0&−5)]Let given matrix be A = [■(3&0&0@0&2&0@0&0&5)] Since all elements are zero except diagonal elements This is a diagonal matrix And, inverse of diagonal matrix is reciprocal of each element on the diagonal Since (b) matches this, let’s test it out Checking Option (b) Let A–1 = [■(1/3&0&0@0&1/2&0@0&0&1/5)] Now, this should be true AA–1 = I Finding AA–1 Putting values [■(3&0&0@0&2&0@0&0&5)] [■(1/3&0&0@0&1/2&0@0&0&1/5)] =[■(3(1/3)+0+0&3(0)+0(1/2)+0&3(0)+0+0(1/5)@0(1/3)+2(0)+0&0+2(1/2)+0&0+2(0)+0(1/5)@0(1/3)+0+5(0)&0+0(1/2)+5(0)&0+0+5(1/5) )] = [■(𝟏&𝟎&𝟎@𝟎&𝟏&𝟎@𝟎&𝟎&𝟏)] = I Thus, for option (b) AA–1 = I So, the correct answer is (B)