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

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

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

Answer:

\[BA= \left[\begin{array}{cccc} -7 & 18 & -22 & -3 \\ 12 & -31 & 38 & 5 \end{array}\right] \]