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Question
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.
Solution
Given that B is a skew-symmetric matrix
∴ B' = – B
Let P = A'BA
⇒ P' = (A'BA)'
= A'B'(A')' .....[(AB)' = B'A']
= A'(– B) A
= – A'BA
= – P
So P' = – P
Hence, A'BA is a skew-symmetric matrix.
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