If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then $A A^{T}=$ _________
The given matrix is $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$.
$\therefore A A^{T}$
$=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]^{T}$
$=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$
$=\left[\begin{array}{lll}1 \times 1 & 1 \times 2 & 1 \times 3 \\ 2 \times 1 & 2 \times 2 & 2 \times 3 \\ 3 \times 1 & 3 \times 2 & 3 \times 3\end{array}\right]$
$=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9\end{array}\right]$
If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then $A A^{T}=$ $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9\end{array}\right]$
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