# How do you multiply matrices given A=((0, 2, 1), (-5, -1, 0)) and B=((1, -4), (0, 1), (5, -1))?

Dec 20, 2016

The answer is $= \left(\begin{matrix}5 & 1 \\ - 5 & 19\end{matrix}\right)$

#### Explanation:

If you have the multiplication of two matrices

$\left(\begin{matrix}a & b & c \\ d & e & f\end{matrix}\right) \cdot \left(\begin{matrix}k & l \\ m & n \\ p & q\end{matrix}\right)$

$= \left(\begin{matrix}a k + b m + c p & a l + b n + c q \\ \mathrm{dk} + e m + f p & \mathrm{dl} + e n + f q\end{matrix}\right)$

Therefore,

$\left(\begin{matrix}0 & 2 & 1 \\ - 5 & - 1 & 0\end{matrix}\right) \cdot \left(\begin{matrix}1 & - 4 \\ 0 & 1 \\ 5 & - 1\end{matrix}\right)$

$= \left(\begin{matrix}5 & 1 \\ - 5 & 19\end{matrix}\right)$