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Question
If A and B are symmetric matrices of same order, prove that AB – BA is a skew-symmetric matrix
Solution
Given A and B are symmetric matrices
⇒ – AT = A and BT = B
To prove AB – BA is a skew-symmetric matrix.
Proof: (AB – BA)T = (AB)T – (BA)T
= BTAT – ATBT
= BA – AB
i.e. (AB – BA)T = – (AB – BA)
⇒ AB – BA is a skew symmetric matrix.
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