Of the following three matrices, only two may be multiplied.

\[ A= \left[\begin{array}{cccc} 1 & 1 & -1 & 2 \\ 0 & 1 & 2 & 0 \end{array}\right] \hspace{1em} B= \left[\begin{array}{cc} 1 & 2 \\ 2 & 5 \\ 2 & 0 \end{array}\right] \hspace{1em} C= \left[\begin{array}{cccc} 1 & 2 & 5 & 6 \\ 0 & 1 & 2 & 3 \\ -1 & -2 & -4 & -5 \end{array}\right] \]

Explain which two can be multiplied and why. Then show how to find their product.

Answer:

\[BA= \left[\begin{array}{cccc} 1 & 3 & 3 & 2 \\ 2 & 7 & 8 & 4 \\ 2 & 2 & -2 & 4 \end{array}\right] \]