Question

If A is a square matrix, then $AA^T$ is a

• A. skew-symmetric matrix
• B. symmetric matrix
• C. diagonal matrix
• D. None of these

Answer 1

Answer: (B)

symmetric matrix

Answer 2

:Let $A=\begin{bmatrix}1&-1&1\\\ 2&1&0\\\ 1&-1&2\end{bmatrix}$, then $A'=\begin{bmatrix}1&2&1\\\ -1&1&-1\\\ 1&0&2\end{bmatrix}$ $\therefore AA'=\begin{bmatrix}1&-1&1\\\ 2&1&0\\\ 1&-1&2\end{bmatrix} \begin{bmatrix}1&2&1\\\ -1&1&-1\\\ 1&0&2\end{bmatrix}=\begin{bmatrix}3&1&4\\\ 1&5&1\\\ 4&1&4\end{bmatrix}$