Of the following three matrices, only two may be multiplied.
\[ A= \left[\begin{array}{cc} 1 & -6 \\ 0 & 1 \\ 1 & -1 \\ 0 & -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{ccc} 0 & -2 & -5 \\ -1 & 6 & 4 \\ 0 & -5 & -4 \\ -1 & 3 & -2 \end{array}\right] \hspace{1em} C= \left[\begin{array}{ccc} 0 & -1 & 1 \\ 1 & 3 & -5 \end{array}\right] \]
Explain which two can be multiplied and why. Then show how to find their product.Answer:
\[AC= \left[\begin{array}{ccc} -6 & -19 & 31 \\ 1 & 3 & -5 \\ -1 & -4 & 6 \\ -1 & -3 & 5 \end{array}\right] \]