Here, we have any square matrix

To Find: AA^T is symmetric or skew – symmetric

Proof: Firstly, we take the transpose of AA^T, so we get

(AA^T)^T = (A^T)^T A^T [∵ (AB)^T = B^TA^T]

⇒ (AA^T)^T = AA^T [∵ (A^T)^T = A]

∴ AA^T is a symmetric matrix