Of the following three matrices, only two may be multiplied.
\[ A= \left[\begin{array}{cccc} 1 & 1 & -3 & -2 \\ 0 & 1 & -4 & -1 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cccc} 1 & 1 & 0 & 1 \\ -2 & -1 & -1 & -1 \\ -1 & 3 & -3 & 5 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cc} 1 & -3 \\ -1 & 4 \\ -1 & 4 \end{array}\right] \]
Explain which two can be multiplied and why. Then show how to find their product.Answer:
\[CA= \left[\begin{array}{cccc} 1 & -2 & 9 & 1 \\ -1 & 3 & -13 & -2 \\ -1 & 3 & -13 & -2 \end{array}\right] \]