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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

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

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