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

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

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

Answer:

\[BC= \left[\begin{array}{ccc} 12 & 21 & -12 \\ 1 & 2 & -1 \\ -8 & -14 & 8 \\ 3 & 5 & -3 \end{array}\right] \]