Answer
$\begin{bmatrix}
5 & 8\\
-4 & -16\\
\end{bmatrix}$
Work Step by Step
First multiply the two leftmost matrices:
$\begin{bmatrix}
3 & 1\\
0 & -2\\
\end{bmatrix}$$\begin{bmatrix}
1 & 0\\
-2 & 2\\
\end{bmatrix}$ = $\begin{bmatrix}
3(1) + 1(-2) & 3(0) + 1(2)\\
0(1) + (-2)(-2) & 0(0) + (-2)(2)\\
\end{bmatrix}$ = $\begin{bmatrix}
3-2 & 0+2\\
0+4 & 0-4\\
\end{bmatrix}$ = $\begin{bmatrix}
1 & 2\\
4 & -4\\
\end{bmatrix}$
We then take the matrix from above and multiply it with the rightmost matrix:
$\begin{bmatrix}
1 & 2\\
4 & -4\\
\end{bmatrix}$$\begin{bmatrix}
1 & 0\\
2 & 4\\
\end{bmatrix}$ = $\begin{bmatrix}
1(1) + 2(2) & 1(0) + 2(4)\\
1(4) + 2(-4) & 4(0) + (-4)(4)\\
\end{bmatrix}$ = $\begin{bmatrix}
1+4 & 0+8\\
4-8 & 0-16\\
\end{bmatrix}$ = $\begin{bmatrix}
5 & 8\\
-4 & -16\\
\end{bmatrix}$
