If A is an 3 × 3 non- singular matrix, such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals to

Question

If A is an 3 × 3 non- singular matrix, such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals to, B - 1 ', I + B, I, B - 1

MARKS App · Accepted Answer

Given, A A ' = A ' A and B = A - 1 A ' B B ' = A - 1 A ' A - 1 A ' ' = A - 1 A ' A ' ' A - 1 ' = A - 1 A ' A A ' - 1 ∵ A ' ' = A , A - 1 ' = A ' - 1 = A - 1 A ' A A ' - 1 = A - 1 A A ' A ' - 1 = A - 1 A A - 1 A ' = I · I = I

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