Question

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

Answer 1

Given $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$
$\Rightarrow$ $A^T=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

$\Rightarrow$ $A{A}^T=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

$\therefore A{A}^T=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right]$