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