Of the following three matrices, only two may be multiplied.
\[ A= \left[\begin{array}{cccc} 1 & 0 & -2 & -3 \\ 0 & 1 & 2 & -2 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} 0 & 1 & 2 \\ -1 & 3 & 4 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cccc} -2 & 3 & 6 & 3 \\ -1 & 1 & 1 & 2 \\ 2 & -1 & 3 & -6 \end{array}\right] \]
Explain which two can be multiplied and why. Then show how to find their product.Answer:
\[BC= \left[\begin{array}{cccc} 3 & -1 & 7 & -10 \\ 7 & -4 & 9 & -21 \end{array}\right] \]