If A = [aij] is a square matrix of order 2 such that aij = {(1,Ā  when i ≠j 0,Ā  when i=jĀ  )┤ , then A2 is :

(a) [8(1 0 1 0)]Ā  (b) [8(1 1 0 0)]Ā  Ā  Ā  (c) [8(1 1 1 0)]Ā  (d) [8(1 0 0 1)]Ā 

Ques 3 (MCQ) - If A = [aij] is a square matrix of order 2 such that - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

part 2 - Question 3 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Question 3 If A = [š‘Žš‘–š‘—] is a square matrix of order 2 such that š‘Žš‘–š‘— = {ā–ˆ(1, š‘¤ā„Žš‘’š‘› š‘– ā‰ š‘—@0, š‘¤ā„Žš‘’š‘› š‘–=š‘— )┤ , then A2 is : (a) [ā– 8(1&0@1&0)] (b) [ā– 8(1&1@0&0)] (c) [ā– 8(1&1@1&0)] (d) [ā– 8(1&0@0&1)] For a 2 Ɨ 2 matrix A = [ā– 8(š‘Ž_11&š‘Ž_12@š‘Ž_21&š‘Ž_22 )] Given that š‘Ž_š‘–š‘—={ā–ˆ(1, š‘–ā‰  š‘—@0, š‘–=š‘—)┤ Thus, š‘Ž_11 = 0, š‘Ž_22 = 0 , š‘Ž_12 = 1, š‘Ž_21 = 1 So, our matrix becomes A = [ā– 8(šŸŽ&šŸ@šŸ&šŸŽ)] Now, A2 = [ā– 8(0&1@1&0)][ā– 8(0&1@1&0)] = [ā– 8(0(0)+1(1)&0(1)+1(0)@1(0)+0(1)&1(1)+0(0))] = [ā– 8(šŸ&šŸŽ@šŸŽ&šŸ)] So, the correct answer is (d)

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