# $\left[\begin{array}{ccc}3 & 2 & 2\\2 & 3 & -2\end{array}\right]\cdot \left[\begin{array}{cc}3 & 2\\2 & 3\\2 & -2\end{array}\right]$

The calculator will multiply the $2$x$3$ matrix $\left[\begin{array}{ccc}3 & 2 & 2\\2 & 3 & -2\end{array}\right]$ by the $3$x$2$ matrix $\left[\begin{array}{cc}3 & 2\\2 & 3\\2 & -2\end{array}\right]$, with steps shown.

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Calculate $\left[\begin{array}{ccc}3 & 2 & 2\\2 & 3 & -2\end{array}\right]\cdot \left[\begin{array}{cc}3 & 2\\2 & 3\\2 & -2\end{array}\right].$
$\left[\begin{array}{ccc}{\color{GoldenRod}3} & {\color{Chartreuse}2} & {\color{OrangeRed}2}\\{\color{SaddleBrown}2} & {\color{DeepPink}3} & {\color{Violet}-2}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Fuchsia}3} & {\color{Peru}2}\\{\color{Red}2} & {\color{OrangeRed}3}\\{\color{Brown}2} & {\color{DarkMagenta}-2}\end{array}\right] = \left[\begin{array}{cc}{\color{GoldenRod}\left(3\right)}\cdot {\color{Fuchsia}\left(3\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{Red}\left(2\right)} + {\color{OrangeRed}\left(2\right)}\cdot {\color{Brown}\left(2\right)} & {\color{GoldenRod}\left(3\right)}\cdot {\color{Peru}\left(2\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{OrangeRed}\left(3\right)} + {\color{OrangeRed}\left(2\right)}\cdot {\color{DarkMagenta}\left(-2\right)}\\{\color{SaddleBrown}\left(2\right)}\cdot {\color{Fuchsia}\left(3\right)} + {\color{DeepPink}\left(3\right)}\cdot {\color{Red}\left(2\right)} + {\color{Violet}\left(-2\right)}\cdot {\color{Brown}\left(2\right)} & {\color{SaddleBrown}\left(2\right)}\cdot {\color{Peru}\left(2\right)} + {\color{DeepPink}\left(3\right)}\cdot {\color{OrangeRed}\left(3\right)} + {\color{Violet}\left(-2\right)}\cdot {\color{DarkMagenta}\left(-2\right)}\end{array}\right] = \left[\begin{array}{cc}17 & 8\\8 & 17\end{array}\right]$
$\left[\begin{array}{ccc}3 & 2 & 2\\2 & 3 & -2\end{array}\right]\cdot \left[\begin{array}{cc}3 & 2\\2 & 3\\2 & -2\end{array}\right] = \left[\begin{array}{cc}17 & 8\\8 & 17\end{array}\right]$A