Let A is a matrix of order 3 × 3 defined as A = a i j 3 × 3 , where a i j = l i m x → 0 1 - c o s i x s i n i x t a n j x ∀ 1 ≤ i , j ≤ 3 , then A 2 is equal to

Question

Let A is a matrix of order 3 × 3 defined as A = a i j 3 × 3 , where a i j = l i m x → 0 1 - c o s i x s i n i x t a n j x ∀ 1 ≤ i , j ≤ 3 , then A 2 is equal to, A, 3 2 A, 2 3 A, 1 4 A

MARKS App · Accepted Answer

Applying L' Hospital rule, we get, a i j = 1 2 i j A = 1 2 1 4 1 6 1 1 2 1 3 3 2 3 4 1 2 = 1 2 1 1 2 1 3 2 1 2 3 3 3 2 1 A 2 = 1 4 1 1 2 1 3 2 1 2 3 3 3 2 1 1 1 2 1 3 2 1 2 3 3 3 2 1 = 1 4 3 3 2 3 3 6 3 6 3 9 9 2 3 = 3 2 A

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