Answer
Part A:
$\begin{bmatrix}
19\\
48\\
\end{bmatrix}$
Part B:
Not possible.
Part C:
$\begin{bmatrix}
14 & -8\\
16 & 142\\
\end{bmatrix}$
Work Step by Step
A has 2 rows and 2 columns (2 x 2).
B has 2 rows and 1 column (2 x 1).
Part A:
$\begin{bmatrix}
(-4)(-6) + (-1)(5)\\
2(-6) + 12(5)\\
\end{bmatrix}$ = $\begin{bmatrix}
24 - 5\\
-12 + 60\\
\end{bmatrix}$ = $\begin{bmatrix}
19\\
48\\
\end{bmatrix}$
Part B:
Since the number of columns in B does not equal the number of rows in A, BA is not possible.
Part C:
$\begin{bmatrix}
(-4)(-4) + (-1)(2) & (-4)(-1) + (-1)(12)\\
2(-4) + 12(2) & 2(-1) + 12(12)\\
\end{bmatrix}$ = $\begin{bmatrix}
16 - 2 & 4 - 12\\
-8 + 24 & -2 + 144\\
\end{bmatrix}$ = $\begin{bmatrix}
14 & -8\\
16 & 142\\
\end{bmatrix}$
