Of the following three matrices, only two may be multiplied.
\[ A= \left[\begin{array}{cccc} 1 & 4 & -1 & 0 \\ -1 & -4 & 2 & -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} 1 & -1 & -4 \\ 2 & -1 & -5 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cccc} 1 & -5 & 5 & 5 \\ 1 & -4 & 3 & 3 \\ 1 & -5 & 6 & 6 \end{array}\right] \]
Explain which two can be multiplied and why. Then show how to find their product.Answer:
\[BC= \left[\begin{array}{cccc} -4 & 19 & -22 & -22 \\ -4 & 19 & -23 & -23 \end{array}\right] \]