Let A = a i j and B = b i j be two 3 × 3 real matrices such that b i j = 3 i + j - 2 a i j , where i , j = 1,2 , 3 . If the determinant of B is 81 , then determinant of A i s

Question

Let A = a i j and B = b i j be two 3 × 3 real matrices such that b i j = 3 i + j - 2 a i j , where i , j = 1,2 , 3 . If the determinant of B is 81 , then determinant of A i s, 1 3, 3, 1 81, 1 9

MARKS App · Accepted Answer

B = b 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 = 3 0 a 11 3 1 a 12 3 2 a 13 3 1 a 21 3 2 a 22 3 3 a 23 3 2 a 31 3 3 a 32 3 4 a 33 ⇒ 81 = 3 3 ∙ 3 ∙ 3 2 A ⇒ 3 4 = 3 6 A ⇒ A = 1 9

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