# Matrix Multiplication Calculator

## Multiply matrices step by step

The calculator will find the product of two matrices (if possible), with steps shown. It multiplies matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Related calculator: Matrix Calculator

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### Your Input

Calculate $\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\end{array}\right]\cdot \left[\begin{array}{cc}2 & 3\\8 & 9\\1 & 1\end{array}\right].$

### Solution

$\left[\begin{array}{ccc}{\color{Crimson}4} & {\color{DeepPink}5} & {\color{Purple}7}\\{\color{Blue}2} & {\color{Violet}1} & {\color{Brown}0}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{Red}2} & {\color{Blue}3}\\{\color{Green}8} & {\color{Violet}9}\\{\color{GoldenRod}1} & {\color{Chartreuse}1}\end{array}\right] = \left[\begin{array}{cc}{\color{Crimson}\left(4\right)}\cdot {\color{Red}\left(2\right)} + {\color{DeepPink}\left(5\right)}\cdot {\color{Green}\left(8\right)} + {\color{Purple}\left(7\right)}\cdot {\color{GoldenRod}\left(1\right)} & {\color{Crimson}\left(4\right)}\cdot {\color{Blue}\left(3\right)} + {\color{DeepPink}\left(5\right)}\cdot {\color{Violet}\left(9\right)} + {\color{Purple}\left(7\right)}\cdot {\color{Chartreuse}\left(1\right)}\\{\color{Blue}\left(2\right)}\cdot {\color{Red}\left(2\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Green}\left(8\right)} + {\color{Brown}\left(0\right)}\cdot {\color{GoldenRod}\left(1\right)} & {\color{Blue}\left(2\right)}\cdot {\color{Blue}\left(3\right)} + {\color{Violet}\left(1\right)}\cdot {\color{Violet}\left(9\right)} + {\color{Brown}\left(0\right)}\cdot {\color{Chartreuse}\left(1\right)}\end{array}\right] = \left[\begin{array}{cc}55 & 64\\12 & 15\end{array}\right]$

### Answer

$\left[\begin{array}{ccc}4 & 5 & 7\\2 & 1 & 0\end{array}\right]\cdot \left[\begin{array}{cc}2 & 3\\8 & 9\\1 & 1\end{array}\right] = \left[\begin{array}{cc}55 & 64\\12 & 15\end{array}\right]$A