If A and B are square matrices of order 3 such that A A T = 3 B and 2 A B - 1 = 3 A - 1 B , then the value of B 2 16 is equal to

Question

If A and B are square matrices of order 3 such that A A T = 3 B and 2 A B - 1 = 3 A - 1 B , then the value of B 2 16 is equal to,

MARKS App · Accepted Answer

Given, A A T = 3 B Taking determinant on both sides, we get, A A T = 3 3 B ⇒ A 2 = 27 B … 1 Also given, 2 A B - 1 = 3 A - 1 B Taking determinant on both sides, we get, 2 3 A 1 B = 3 3 1 A ⋅ B 2 3 A 2 = 3 3 B 2 … 2 From 1 and 2 , we get, 2 3 27 B = 3 3 B 2 ⇒ B 2 = 8 B ⇒ B = 8

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