Of the following three matrices, only two may be multiplied.

\[ A= \left[\begin{array}{cccc} -1 & 1 & 2 & 0 \\ 2 & -3 & -5 & -2 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} 1 & -2 & 1 \\ 1 & -1 & 2 \\ -1 & -1 & -3 \\ 5 & -6 & 5 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 1 & 3 & -5 \\ -1 & -2 & 4 \end{array}\right] \]

Explain which two can be multiplied and why. Then show how to find their product.

Answer:

\[AB= \left[\begin{array}{ccc} -2 & -1 & -5 \\ -6 & 16 & 1 \end{array}\right] \]