Answer
$\begin{bmatrix} 9&-31\\-6&-3\end{bmatrix}$
Work Step by Step
We are given the matrices:
$B=\begin{bmatrix}4&-3&0\\12&1&-2\end{bmatrix}, C=\begin{bmatrix}3&-4\\1&5\\5&2\end{bmatrix}$
Compute $BC$:
$BC=\begin{bmatrix}4&-3&0\\1&1&-2\end{bmatrix}\times\begin{bmatrix}3&-4\\1&5\\5&2\end{bmatrix}$
$=\begin{bmatrix}4(3)+(-3)(1)+0(5)&4(-4)+(-3)5+0(2)\\1(3)+1(1)+(-2)5&1(-4)+1(5)+(-2)2\end{bmatrix}$
$=\begin{bmatrix} 9&-31\\-6&-3\end{bmatrix}$
