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  4. If A is a square matrix, then AAT is a

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

Matrices

Solution:

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