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

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

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

Answer:

\[BC= \left[\begin{array}{cccc} -3 & -21 & -7 & -16 \\ 4 & 25 & 10 & 17 \end{array}\right] \]