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Class 12
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If A = [aij] is a square matrix of order 2 such that aij = {(1,Β  when i β‰ j 0,Β  when i=jΒ  )─ , then A2 is :

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

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Question 3 If A = [π‘Žπ‘–π‘—] is a square matrix of order 2 such that π‘Žπ‘–π‘— = {β–ˆ(1, π‘€β„Žπ‘’π‘› 𝑖 ≠𝑗@0, π‘€β„Žπ‘’π‘› 𝑖=𝑗 )─ , then A2 is : (a) [β– 8(1&0@1&0)] (b) [β– 8(1&1@0&0)] (c) [β– 8(1&1@1&0)] (d) [β– 8(1&0@0&1)] For a 2 Γ— 2 matrix A = [β– 8(π‘Ž_11&π‘Ž_12@π‘Ž_21&π‘Ž_22 )] Given that π‘Ž_𝑖𝑗={β–ˆ(1, 𝑖≠ 𝑗@0, 𝑖=𝑗)─ Thus, π‘Ž_11 = 0, π‘Ž_22 = 0 , π‘Ž_12 = 1, π‘Ž_21 = 1 So, our matrix becomes A = [β– 8(𝟎&𝟏@𝟏&𝟎)] Now, A2 = [β– 8(0&1@1&0)][β– 8(0&1@1&0)] = [β– 8(0(0)+1(1)&0(1)+1(0)@1(0)+0(1)&1(1)+0(0))] = [β– 8(𝟏&𝟎@𝟎&𝟏)] So, the correct answer is (d)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.