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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{DarkCyan}4} & {\color{Violet}5} & {\color{DarkBlue}7}\\{\color{Crimson}2} & {\color{GoldenRod}1} & {\color{OrangeRed}0}\\{\color{Peru}1} & {\color{Red}2} & {\color{DarkMagenta}3}\end{array}\right]\cdot \left[\begin{array}{ccc}{\color{Peru}- \frac{1}{2}} & {\color{Crimson}0} & {\color{GoldenRod}\frac{1}{2}}\\{\color{Chartreuse}5} & {\color{DeepPink}-1} & {\color{DarkCyan}-1}\\{\color{Green}- \frac{7}{2}} & {\color{Magenta}1} & {\color{Violet}\frac{1}{2}}\end{array}\right] = \left[\begin{array}{ccc}{\color{DarkCyan}\left(4\right)}\cdot {\color{Peru}\left(- \frac{1}{2}\right)} + {\color{Violet}\left(5\right)}\cdot {\color{Chartreuse}\left(5\right)} + {\color{DarkBlue}\left(7\right)}\cdot {\color{Green}\left(- \frac{7}{2}\right)} & {\color{DarkCyan}\left(4\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{Violet}\left(5\right)}\cdot {\color{DeepPink}\left(-1\right)} + {\color{DarkBlue}\left(7\right)}\cdot {\color{Magenta}\left(1\right)} & {\color{DarkCyan}\left(4\right)}\cdot {\color{GoldenRod}\left(\frac{1}{2}\right)} + {\color{Violet}\left(5\right)}\cdot {\color{DarkCyan}\left(-1\right)} + {\color{DarkBlue}\left(7\right)}\cdot {\color{Violet}\left(\frac{1}{2}\right)}\\{\color{Crimson}\left(2\right)}\cdot {\color{Peru}\left(- \frac{1}{2}\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{Chartreuse}\left(5\right)} + {\color{OrangeRed}\left(0\right)}\cdot {\color{Green}\left(- \frac{7}{2}\right)} & {\color{Crimson}\left(2\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{DeepPink}\left(-1\right)} + {\color{OrangeRed}\left(0\right)}\cdot {\color{Magenta}\left(1\right)} & {\color{Crimson}\left(2\right)}\cdot {\color{GoldenRod}\left(\frac{1}{2}\right)} + {\color{GoldenRod}\left(1\right)}\cdot {\color{DarkCyan}\left(-1\right)} + {\color{OrangeRed}\left(0\right)}\cdot {\color{Violet}\left(\frac{1}{2}\right)}\\{\color{Peru}\left(1\right)}\cdot {\color{Peru}\left(- \frac{1}{2}\right)} + {\color{Red}\left(2\right)}\cdot {\color{Chartreuse}\left(5\right)} + {\color{DarkMagenta}\left(3\right)}\cdot {\color{Green}\left(- \frac{7}{2}\right)} & {\color{Peru}\left(1\right)}\cdot {\color{Crimson}\left(0\right)} + {\color{Red}\left(2\right)}\cdot {\color{DeepPink}\left(-1\right)} + {\color{DarkMagenta}\left(3\right)}\cdot {\color{Magenta}\left(1\right)} & {\color{Peru}\left(1\right)}\cdot {\color{GoldenRod}\left(\frac{1}{2}\right)} + {\color{Red}\left(2\right)}\cdot {\color{DarkCyan}\left(-1\right)} + {\color{DarkMagenta}\left(3\right)}\cdot {\color{Violet}\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