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$$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$

The calculator will multiply the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]$$$ by the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right]$$$, with steps shown.

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Your Input

Calculate $$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right].$$$

Solution

$$$\left[\begin{array}{ccc}{\color{Green}0} & {\color{Magenta}1} & {\color{Peru}1}\\{\color{DarkMagenta}\sqrt{2}} & {\color{DeepPink}2} & {\color{DarkCyan}0}\\{\color{SaddleBrown}0} & {\color{Red}1} & {\color{Chartreuse}1}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{DeepPink}0} & {\color{Peru}\sqrt{2}} & {\color{DarkMagenta}0}\\{\color{SaddleBrown}1} & {\color{Magenta}2} & {\color{DarkCyan}1}\\{\color{Chocolate}1} & {\color{BlueViolet}0} & {\color{Violet}1}\end{array}\right] = \left[\begin{array}{ccc}{\color{Green}\left(0\right)}\cdot {\color{DeepPink}\left(0\right)} + {\color{Magenta}\left(1\right)}\cdot {\color{SaddleBrown}\left(1\right)} + {\color{Peru}\left(1\right)}\cdot {\color{Chocolate}\left(1\right)} & {\color{Green}\left(0\right)}\cdot {\color{Peru}\left(\sqrt{2}\right)} + {\color{Magenta}\left(1\right)}\cdot {\color{Magenta}\left(2\right)} + {\color{Peru}\left(1\right)}\cdot {\color{BlueViolet}\left(0\right)} & {\color{Green}\left(0\right)}\cdot {\color{DarkMagenta}\left(0\right)} + {\color{Magenta}\left(1\right)}\cdot {\color{DarkCyan}\left(1\right)} + {\color{Peru}\left(1\right)}\cdot {\color{Violet}\left(1\right)}\\{\color{DarkMagenta}\left(\sqrt{2}\right)}\cdot {\color{DeepPink}\left(0\right)} + {\color{DeepPink}\left(2\right)}\cdot {\color{SaddleBrown}\left(1\right)} + {\color{DarkCyan}\left(0\right)}\cdot {\color{Chocolate}\left(1\right)} & {\color{DarkMagenta}\left(\sqrt{2}\right)}\cdot {\color{Peru}\left(\sqrt{2}\right)} + {\color{DeepPink}\left(2\right)}\cdot {\color{Magenta}\left(2\right)} + {\color{DarkCyan}\left(0\right)}\cdot {\color{BlueViolet}\left(0\right)} & {\color{DarkMagenta}\left(\sqrt{2}\right)}\cdot {\color{DarkMagenta}\left(0\right)} + {\color{DeepPink}\left(2\right)}\cdot {\color{DarkCyan}\left(1\right)} + {\color{DarkCyan}\left(0\right)}\cdot {\color{Violet}\left(1\right)}\\{\color{SaddleBrown}\left(0\right)}\cdot {\color{DeepPink}\left(0\right)} + {\color{Red}\left(1\right)}\cdot {\color{SaddleBrown}\left(1\right)} + {\color{Chartreuse}\left(1\right)}\cdot {\color{Chocolate}\left(1\right)} & {\color{SaddleBrown}\left(0\right)}\cdot {\color{Peru}\left(\sqrt{2}\right)} + {\color{Red}\left(1\right)}\cdot {\color{Magenta}\left(2\right)} + {\color{Chartreuse}\left(1\right)}\cdot {\color{BlueViolet}\left(0\right)} & {\color{SaddleBrown}\left(0\right)}\cdot {\color{DarkMagenta}\left(0\right)} + {\color{Red}\left(1\right)}\cdot {\color{DarkCyan}\left(1\right)} + {\color{Chartreuse}\left(1\right)}\cdot {\color{Violet}\left(1\right)}\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$

Answer

$$$\left[\begin{array}{ccc}0 & 1 & 1\\\sqrt{2} & 2 & 0\\0 & 1 & 1\end{array}\right]\cdot \left[\begin{array}{ccc}0 & \sqrt{2} & 0\\1 & 2 & 1\\1 & 0 & 1\end{array}\right] = \left[\begin{array}{ccc}2 & 2 & 2\\2 & 6 & 2\\2 & 2 & 2\end{array}\right]$$$A