If A = [aij] is a square matrix of order 2 such that aij = {(1, when i ≠j 0, when i=j )โค , then A2 is :
(a) [8(1 0 1 0)] (b) [8(1 1 0 0)] (c) [8(1 1 1 0)] (d) [8(1 0 0 1)]
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Last updated at Sept. 4, 2021 by Teachoo
Transcript
Question 3 If A = [๐๐๐] is a square matrix of order 2 such that ๐๐๐ = {โ(1, ๐คโ๐๐ ๐ โ ๐@0, ๐คโ๐๐ ๐=๐ )โค , then A2 is : (a) [โ 8(1&0@1&0)] (b) [โ 8(1&1@0&0)] (c) [โ 8(1&1@1&0)] (d) [โ 8(1&0@0&1)] For a 2 ร 2 matrix A = [โ 8(๐_11&๐_12@๐_21&๐_22 )] Given that ๐_๐๐={โ(1, ๐โ ๐@0, ๐=๐)โค Thus, ๐_11 = 0, ๐_22 = 0 , ๐_12 = 1, ๐_21 = 1 So, our matrix becomes A = [โ 8(๐&๐@๐&๐)] Now, A2 = [โ 8(0&1@1&0)][โ 8(0&1@1&0)] = [โ 8(0(0)+1(1)&0(1)+1(0)@1(0)+0(1)&1(1)+0(0))] = [โ 8(๐&๐@๐&๐)] So, the correct answer is (d)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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