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

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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Your Input

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

Solution

$$$\left[\begin{array}{ccc}{\color{Peru}3} & {\color{BlueViolet}2} & {\color{DeepPink}2}\\{\color{Red}2} & {\color{Fuchsia}3} & {\color{DarkCyan}-2}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{GoldenRod}3} & {\color{Chocolate}2}\\{\color{Purple}2} & {\color{DeepPink}3}\\{\color{SaddleBrown}2} & {\color{Green}-2}\end{array}\right] = \left[\begin{array}{cc}{\color{Peru}\left(3\right)}\cdot {\color{GoldenRod}\left(3\right)} + {\color{BlueViolet}\left(2\right)}\cdot {\color{Purple}\left(2\right)} + {\color{DeepPink}\left(2\right)}\cdot {\color{SaddleBrown}\left(2\right)} & {\color{Peru}\left(3\right)}\cdot {\color{Chocolate}\left(2\right)} + {\color{BlueViolet}\left(2\right)}\cdot {\color{DeepPink}\left(3\right)} + {\color{DeepPink}\left(2\right)}\cdot {\color{Green}\left(-2\right)}\\{\color{Red}\left(2\right)}\cdot {\color{GoldenRod}\left(3\right)} + {\color{Fuchsia}\left(3\right)}\cdot {\color{Purple}\left(2\right)} + {\color{DarkCyan}\left(-2\right)}\cdot {\color{SaddleBrown}\left(2\right)} & {\color{Red}\left(2\right)}\cdot {\color{Chocolate}\left(2\right)} + {\color{Fuchsia}\left(3\right)}\cdot {\color{DeepPink}\left(3\right)} + {\color{DarkCyan}\left(-2\right)}\cdot {\color{Green}\left(-2\right)}\end{array}\right] = \left[\begin{array}{cc}17 & 8\\8 & 17\end{array}\right]$$$

Answer

$$$\left[\begin{array}{ccc}3 & 2 & 2\\2 & 3 & -2\end{array}\right]\cdot \left[\begin{array}{cc}3 & 2\\2 & 3\\2 & -2\end{array}\right] = \left[\begin{array}{cc}17 & 8\\8 & 17\end{array}\right]$$$A