Answer
$AB=\begin{bmatrix}1&-7\\-2&14\end{bmatrix}$
$AC=\begin{bmatrix}1&-7\\-2&14\end{bmatrix}$
$AB=AC$ $\star$
$\begin{bmatrix}8&4\\5&5\end{bmatrix}\neq\begin{bmatrix}5&-2\\3&1\end{bmatrix}$ $\star$
Work Step by Step
The row-column rule for matrix products gives the following:
$AB=\begin{bmatrix}16-15&8-15\\-32+30&-16+30\end{bmatrix}$
$AC=\begin{bmatrix}10-9&-4-3\\-20+18&8+6\end{bmatrix}$
Simplifying, we see that these matrix products are equal, although $B$ and $C$ are not equal. This disproves the cancellation law for matrix multiplication.
