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If A and B are symmetric matrices, prove...

If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.

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To prove that \( AB - BA \) is a skew symmetric matrix when \( A \) and \( B \) are symmetric matrices, we will follow these steps: **Step 1: Understand the definitions** - A matrix \( P \) is symmetric if \( P^T = P \). - A matrix \( Q \) is skew symmetric if \( Q^T = -Q \). **Step 2: Given that \( A \) and \( B \) are symmetric** - This means \( A^T = A \) and \( B^T = B \). ...
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