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Question
For any square matrix write whether AAT is symmetric or skew-symmetric.
Solution
Here,
\[\left( A A^T \right)^T = \left( A^T \right)^T A^T \left[ \because \left( AB \right)^T = B^T A^T \right]\]
\[ \Rightarrow \left( A A^T \right)^T = A A^T \left[ \because \left( A^T \right)^T = A \right] \]
Thus, AAT is a symmetric matrix.
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