If A is a 3 × 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals, where X ' denotes the transpose of the matrix X .

Question

If A is a 3 × 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals, where X ' denotes the transpose of the matrix X ., B - 1, B - 1 ', I + B, I

MARKS App · Accepted Answer

A ' = A T A A ' = A ' A B = A - 1 A ' B ' = A - 1 A ' ' = A ' ' · A - 1 ' = A A - 1 ' B B ' = A - 1 A ' · A A - 1 ' = A - 1 · A · A ' · A - 1 ' ∵ A A ' = A ' A = I · A ' · A - 1 ' = I · A - 1 A ' ∵ C D ' = D ' C ' = I · I ' = I 2 ∵ I = I ' = I

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