$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$

The calculator will multiply the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$ by the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]$$$, with steps shown.

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Calculate $$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right].$$$

Solution

$$$\left[\begin{array}{ccc}{\color{Peru}1} & {\color{Purple}3} & {\color{DarkBlue}4}\\{\color{Brown}-1} & {\color{Chocolate}-8} & {\color{DeepPink}5}\\{\color{Blue}0} & {\color{Red}6} & {\color{Magenta}-7}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{DeepPink}1} & {\color{Violet}3} & {\color{Chartreuse}4}\\{\color{Red}-1} & {\color{DarkMagenta}-8} & {\color{SaddleBrown}5}\\{\color{DarkCyan}0} & {\color{Green}6} & {\color{DarkBlue}-7}\end{array}\right] = \left[\begin{array}{ccc}{\color{Peru}\left(1\right)}\cdot {\color{DeepPink}\left(1\right)} + {\color{Purple}\left(3\right)}\cdot {\color{Red}\left(-1\right)} + {\color{DarkBlue}\left(4\right)}\cdot {\color{DarkCyan}\left(0\right)} & {\color{Peru}\left(1\right)}\cdot {\color{Violet}\left(3\right)} + {\color{Purple}\left(3\right)}\cdot {\color{DarkMagenta}\left(-8\right)} + {\color{DarkBlue}\left(4\right)}\cdot {\color{Green}\left(6\right)} & {\color{Peru}\left(1\right)}\cdot {\color{Chartreuse}\left(4\right)} + {\color{Purple}\left(3\right)}\cdot {\color{SaddleBrown}\left(5\right)} + {\color{DarkBlue}\left(4\right)}\cdot {\color{DarkBlue}\left(-7\right)}\\{\color{Brown}\left(-1\right)}\cdot {\color{DeepPink}\left(1\right)} + {\color{Chocolate}\left(-8\right)}\cdot {\color{Red}\left(-1\right)} + {\color{DeepPink}\left(5\right)}\cdot {\color{DarkCyan}\left(0\right)} & {\color{Brown}\left(-1\right)}\cdot {\color{Violet}\left(3\right)} + {\color{Chocolate}\left(-8\right)}\cdot {\color{DarkMagenta}\left(-8\right)} + {\color{DeepPink}\left(5\right)}\cdot {\color{Green}\left(6\right)} & {\color{Brown}\left(-1\right)}\cdot {\color{Chartreuse}\left(4\right)} + {\color{Chocolate}\left(-8\right)}\cdot {\color{SaddleBrown}\left(5\right)} + {\color{DeepPink}\left(5\right)}\cdot {\color{DarkBlue}\left(-7\right)}\\{\color{Blue}\left(0\right)}\cdot {\color{DeepPink}\left(1\right)} + {\color{Red}\left(6\right)}\cdot {\color{Red}\left(-1\right)} + {\color{Magenta}\left(-7\right)}\cdot {\color{DarkCyan}\left(0\right)} & {\color{Blue}\left(0\right)}\cdot {\color{Violet}\left(3\right)} + {\color{Red}\left(6\right)}\cdot {\color{DarkMagenta}\left(-8\right)} + {\color{Magenta}\left(-7\right)}\cdot {\color{Green}\left(6\right)} & {\color{Blue}\left(0\right)}\cdot {\color{Chartreuse}\left(4\right)} + {\color{Red}\left(6\right)}\cdot {\color{SaddleBrown}\left(5\right)} + {\color{Magenta}\left(-7\right)}\cdot {\color{DarkBlue}\left(-7\right)}\end{array}\right] = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$

Answer

$$$\left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right]\cdot \left[\begin{array}{ccc}1 & 3 & 4\\-1 & -8 & 5\\0 & 6 & -7\end{array}\right] = \left[\begin{array}{ccc}-2 & 3 & -9\\7 & 91 & -79\\-6 & -90 & 79\end{array}\right]$$$A