Question

For any square matrix write whether AA^T is symmetric or skew-symmetric.

Answer 1

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, AA^T is a symmetric matrix.