Answer
$\begin{bmatrix}-13&1\\-21&9\\25&-13\end{bmatrix}$
Work Step by Step
We are given the matrices:
$$A=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix},\text{ }B=\begin{bmatrix}3&2\\-2&-1\end{bmatrix}, \text{ }C=\begin{bmatrix}-4&5\\1&0\end{bmatrix}.$$
Calculate $A(B-C)$:
$$\begin{align*}
A(B-C)&=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix}\left(\begin{bmatrix}3&2\\-2&-1\end{bmatrix}-\begin{bmatrix}-4&5\\1&0\end{bmatrix}\right)\\
&=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix}\cdot\begin{bmatrix}3-(-4)&2-5\\-2-1&-1-0\end{bmatrix}\\
&=\begin{bmatrix}-1&2\\-3&0\\4&1\end{bmatrix}\cdot\begin{bmatrix}7&-3\\-3&-1\end{bmatrix}\\
&=\begin{bmatrix}(-1)7+2(-3)&(-1)(-3)+2(-1)\\(-3)7+0(-3)&(-3)(-3)+0(-1)\\4(7)+1(-3)&4(-3)+1(-1)&\end{bmatrix}\\
&=\begin{bmatrix}-13&1\\-21&9\\25&-13\end{bmatrix}.
\end{align*}$$
