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

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

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

Answer:

\[BA= \left[\begin{array}{cc} 27 & 28 \\ 7 & 31 \\ 10 & 18 \\ 7 & 3 \end{array}\right] \]