Answer
$\left[\begin{array}{ll}
24 & 0\\
-33 & -5\\
-3 & -1
\end{array}\right]$
Work Step by Step
The product of an $m\times\underline{n}$ matrix $A$ and an $\underline{n}\times p$ matrix $B$
is an $m\times p$ matrix $AB$.
The element in the ith row and $j\mathrm{t}\mathrm{h}$ column of $AB$ is found by
multiplying each element in the ith row of $A$ by the corresponding element in the $j\mathrm{t}\mathrm{h}$ column of $B$
and adding the products.
-----------------
B and C are both $2\times 2$ matrices, so their sum exists.
$A$ is a $3\times\underline{2}$ matrix, $(B+C)$ is a $\underline{2}\times 2$ matrix
$A(B+C)$ exists, and is a $3\times 2$ matrix.
$B+C=\left[\begin{array}{ll}
5+1 & 1-1\\
-2-1 & -2+1
\end{array}\right]=\left[\begin{array}{ll}
6 & 0\\
-3 & -1
\end{array}\right]$
$A(B+C)=\left[\begin{array}{ll}
4 & 0\\
-3 & 5\\
0 & 1
\end{array}\right]\cdot\left[\begin{array}{ll}
6 & 0\\
-3 & -1
\end{array}\right]=$
$=\left[\begin{array}{ll}
4(6)+0(-3) & 4(0)+0(-1)\\
-3(6)+5(-3) & -3(0)+5(-1)\\
0(6)+1(-3) & 0(0)+1(-1)
\end{array}\right]$
$=\left[\begin{array}{ll}
24 & 0\\
-33 & -5\\
-3 & -1
\end{array}\right]$
