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$$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\\1 & 2 & 3\end{array}\right]\cdot \left[\begin{array}{ccc}- \frac{1}{2} & 0 & \frac{1}{2}\\5 & -1 & -1\\- \frac{7}{2} & 1 & \frac{1}{2}\end{array}\right]$$$

The calculator will multiply the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\\1 & 2 & 3\end{array}\right]$$$ by the $$$3$$$x$$$3$$$ matrix $$$\left[\begin{array}{ccc}- \frac{1}{2} & 0 & \frac{1}{2}\\5 & -1 & -1\\- \frac{7}{2} & 1 & \frac{1}{2}\end{array}\right]$$$, with steps shown.

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Your Input

Calculate $$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\\1 & 2 & 3\end{array}\right]\cdot \left[\begin{array}{ccc}- \frac{1}{2} & 0 & \frac{1}{2}\\5 & -1 & -1\\- \frac{7}{2} & 1 & \frac{1}{2}\end{array}\right].$$$

Solution

$$$\left[\begin{array}{ccc}{\color{Crimson}4} & {\color{Magenta}5} & {\color{Brown}7}\\{\color{Fuchsia}2} & {\color{DarkCyan}1} & {\color{GoldenRod}0}\\{\color{DeepPink}1} & {\color{Chartreuse}2} & {\color{Green}3}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{Green}- \frac{1}{2}} & {\color{SaddleBrown}0} & {\color{Purple}\frac{1}{2}}\\{\color{DarkMagenta}5} & {\color{Blue}-1} & {\color{Chartreuse}-1}\\{\color{Chocolate}- \frac{7}{2}} & {\color{Brown}1} & {\color{Red}\frac{1}{2}}\end{array}\right] = \left[\begin{array}{ccc}{\color{Crimson}\left(4\right)}\cdot {\color{Green}\left(- \frac{1}{2}\right)} + {\color{Magenta}\left(5\right)}\cdot {\color{DarkMagenta}\left(5\right)} + {\color{Brown}\left(7\right)}\cdot {\color{Chocolate}\left(- \frac{7}{2}\right)} & {\color{Crimson}\left(4\right)}\cdot {\color{SaddleBrown}\left(0\right)} + {\color{Magenta}\left(5\right)}\cdot {\color{Blue}\left(-1\right)} + {\color{Brown}\left(7\right)}\cdot {\color{Brown}\left(1\right)} & {\color{Crimson}\left(4\right)}\cdot {\color{Purple}\left(\frac{1}{2}\right)} + {\color{Magenta}\left(5\right)}\cdot {\color{Chartreuse}\left(-1\right)} + {\color{Brown}\left(7\right)}\cdot {\color{Red}\left(\frac{1}{2}\right)}\\{\color{Fuchsia}\left(2\right)}\cdot {\color{Green}\left(- \frac{1}{2}\right)} + {\color{DarkCyan}\left(1\right)}\cdot {\color{DarkMagenta}\left(5\right)} + {\color{GoldenRod}\left(0\right)}\cdot {\color{Chocolate}\left(- \frac{7}{2}\right)} & {\color{Fuchsia}\left(2\right)}\cdot {\color{SaddleBrown}\left(0\right)} + {\color{DarkCyan}\left(1\right)}\cdot {\color{Blue}\left(-1\right)} + {\color{GoldenRod}\left(0\right)}\cdot {\color{Brown}\left(1\right)} & {\color{Fuchsia}\left(2\right)}\cdot {\color{Purple}\left(\frac{1}{2}\right)} + {\color{DarkCyan}\left(1\right)}\cdot {\color{Chartreuse}\left(-1\right)} + {\color{GoldenRod}\left(0\right)}\cdot {\color{Red}\left(\frac{1}{2}\right)}\\{\color{DeepPink}\left(1\right)}\cdot {\color{Green}\left(- \frac{1}{2}\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{DarkMagenta}\left(5\right)} + {\color{Green}\left(3\right)}\cdot {\color{Chocolate}\left(- \frac{7}{2}\right)} & {\color{DeepPink}\left(1\right)}\cdot {\color{SaddleBrown}\left(0\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{Blue}\left(-1\right)} + {\color{Green}\left(3\right)}\cdot {\color{Brown}\left(1\right)} & {\color{DeepPink}\left(1\right)}\cdot {\color{Purple}\left(\frac{1}{2}\right)} + {\color{Chartreuse}\left(2\right)}\cdot {\color{Chartreuse}\left(-1\right)} + {\color{Green}\left(3\right)}\cdot {\color{Red}\left(\frac{1}{2}\right)}\end{array}\right] = \left[\begin{array}{ccc}- \frac{3}{2} & 2 & \frac{1}{2}\\4 & -1 & 0\\-1 & 1 & 0\end{array}\right]$$$

Answer

$$$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\\1 & 2 & 3\end{array}\right]\cdot \left[\begin{array}{ccc}- \frac{1}{2} & 0 & \frac{1}{2}\\5 & -1 & -1\\- \frac{7}{2} & 1 & \frac{1}{2}\end{array}\right] = \left[\begin{array}{ccc}- \frac{3}{2} & 2 & \frac{1}{2}\\4 & -1 & 0\\-1 & 1 & 0\end{array}\right] = \left[\begin{array}{ccc}-1.5 & 2 & 0.5\\4 & -1 & 0\\-1 & 1 & 0\end{array}\right]$$$A