Question

If $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$, write AA^T.

Answer 1

$$\begin{gathered} \mathrm{Given}:A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right] \\ {A}^T=\left[\begin{array}{ccc}1& 2& 3\end{array}\right] \\ \mathrm{Now}, \\ A{A}^T=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right] \\ \Rightarrow A{A}^T=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right] \end{gathered}$$