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$$$\left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]\cdot \left[\begin{array}{cc}e & 0\\0 & e^{-2}\end{array}\right]$$$

The calculator will multiply the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]$$$ by the $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}e & 0\\0 & e^{-2}\end{array}\right]$$$, with steps shown.

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Your Input

Calculate $$$\left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]\cdot \left[\begin{array}{cc}e & 0\\0 & e^{-2}\end{array}\right].$$$

Solution

$$$\left[\begin{array}{cc}{\color{Blue}5} & {\color{Brown}2}\\{\color{SaddleBrown}1} & {\color{GoldenRod}1}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Green}e} & {\color{SaddleBrown}0}\\{\color{DarkCyan}0} & {\color{Chartreuse}e^{-2}}\end{array}\right] = \left[\begin{array}{cc}{\color{Blue}\left(5\right)}\cdot {\color{Green}\left(e\right)} + {\color{Brown}\left(2\right)}\cdot {\color{DarkCyan}\left(0\right)} & {\color{Blue}\left(5\right)}\cdot {\color{SaddleBrown}\left(0\right)} + {\color{Brown}\left(2\right)}\cdot {\color{Chartreuse}\left(e^{-2}\right)}\\{\color{SaddleBrown}\left(1\right)}\cdot {\color{Green}\left(e\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{DarkCyan}\left(0\right)} & {\color{SaddleBrown}\left(1\right)}\cdot {\color{SaddleBrown}\left(0\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{Chartreuse}\left(e^{-2}\right)}\end{array}\right] = \left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]$$$

Answer

$$$\left[\begin{array}{cc}5 & 2\\1 & 1\end{array}\right]\cdot \left[\begin{array}{cc}e & 0\\0 & e^{-2}\end{array}\right] = \left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\approx \left[\begin{array}{cc}13.591409142295226 & 0.270670566473225\\2.718281828459045 & 0.135335283236613\end{array}\right]$$$A