If A = [aij] is a square matrix of order 2 such that aij = {(1,  when i ≠j 0,  when i=j  )โ”ค , 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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  1. Class 12
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Transcript

Question 3 If A = [๐‘Ž๐‘–๐‘—] is a square matrix of order 2 such that ๐‘Ž๐‘–๐‘— = {โ–ˆ(1, ๐‘คโ„Ž๐‘’๐‘› ๐‘– โ‰ ๐‘—@0, ๐‘คโ„Ž๐‘’๐‘› ๐‘–=๐‘— )โ”ค , 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‘Ž_11&๐‘Ž_12@๐‘Ž_21&๐‘Ž_22 )] Given that ๐‘Ž_๐‘–๐‘—={โ–ˆ(1, ๐‘–โ‰  ๐‘—@0, ๐‘–=๐‘—)โ”ค Thus, ๐‘Ž_11 = 0, ๐‘Ž_22 = 0 , ๐‘Ž_12 = 1, ๐‘Ž_21 = 1 So, our matrix becomes A = [โ– 8(๐ŸŽ&๐Ÿ@๐Ÿ&๐ŸŽ)] 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Ÿ&๐ŸŽ@๐ŸŽ&๐Ÿ)] So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.