Of the following three matrices, only two may be multiplied.
\[ A= \left[\begin{array}{ccc} 0 & -1 & -2 \\ -2 & -5 & 2 \\ 1 & 0 & 0 \\ -1 & -4 & -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} -1 & -5 \\ 2 & -5 \\ 1 & 1 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 & 2 \\ -2 & -3 \\ -3 & -1 \\ 5 & 6 \end{array}\right] \]
Explain which two can be multiplied and why. Then show how to find their product.Answer:
\[AB= \left[\begin{array}{cc} -4 & 3 \\ -6 & 37 \\ -1 & -5 \\ -8 & 24 \end{array}\right] \]