Answer
$ \left[\begin{array}{ll}
16 & -16\\
-12 & 12\\
0 & 0
\end{array}\right]$
Work Step by Step
A product of two matrices exists
if the first has as many columns
as the second matrix has rows.
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 product BC exists because B is a 2$\times\underline{2}$ matrix,
and C is a $\underline{2}\times$2 matrix.
(BC) is 2$\times$2.
The product of A ( a $3\times\underline{2}$ matrix) and BC ( a $\underline{2}\times$2 matrix)
exists and is a $3\times 2$ matrix.
$BC=\left[\begin{array}{ll}
5(1)+1(-1) & 5(-1)+1(1)\\
-2(1)-2(-1) & -2(1)-2(-1)
\end{array}\right] =\left[\begin{array}{ll}
4 & -4\\
0 & 0
\end{array}\right]$
$A(BC)=\left[\begin{array}{ll}
4 & 0\\
-3 & 5\\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
4 & -4\\
0 & 0
\end{array}\right]$
$=\left[\begin{array}{ll}
16+0 & -16+0\\
-12+0 & 12+0\\
0+0 & 0+0
\end{array}\right]$
$=\left[\begin{array}{ll}
16 & -16\\
-12 & 12\\
0 & 0
\end{array}\right]$
