# How do you multiply ((3, -2), (-1, 1)) with ((3, 1), (-2, 4)) with ((-2, 4), (1, 3))?

Nov 10, 2016

The answer is $= \left(\begin{matrix}- 31 & 37 \\ 13 & - 11\end{matrix}\right)$

#### Explanation:

The product of two 2x2 matrices is
$\left(\begin{matrix}a & b \\ c & d\end{matrix}\right) \cdot \left(\begin{matrix}e & f \\ g & h\end{matrix}\right) = \left(\begin{matrix}a e + b g & a f + b h \\ c e + \mathrm{dg} & c f + \mathrm{dh}\end{matrix}\right)$

$\left(\begin{matrix}3 & - 2 \\ - 1 & 1\end{matrix}\right) \left(\begin{matrix}3 & 1 \\ - 2 & 4\end{matrix}\right) = \left(\begin{matrix}9 + 4 & 3 - 8 \\ - 3 - 2 & - 1 + 4\end{matrix}\right)$

$\left(\begin{matrix}13 & - 5 \\ - 5 & 3\end{matrix}\right)$

and the second multiplication is

$\left(\begin{matrix}13 & - 5 \\ - 5 & 3\end{matrix}\right) \cdot \left(\begin{matrix}- 2 & 4 \\ 1 & 3\end{matrix}\right) = \left(\begin{matrix}- 26 - 5 & 52 - 15 \\ 10 + 3 & - 20 + 9\end{matrix}\right)$

$\left(\begin{matrix}- 31 & 37 \\ 13 & - 11\end{matrix}\right)$