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{\bf Question}

Let $$A = \left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 3 & 2
\end{array} \right) \hspace{.2in} B = \left( \begin{array}{cc}
1 & -1 \\ 2 & -3 \\ 0 & -1 \end{array} \right) \hspace{.2in} C =
\left( \begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & 0 \\ 3 & -4 & 2
\end{array} \right).$$ Evaluate all possible products of pairs of
the above matrices.

\vspace{.25in}

{\bf Answer}

$AA$ is undefined

$AB = \left( \begin{array}{cc} 5 & -10 \\ 10 & -15 \end{array}
\right)$

$AC = \left( \begin{array}{ccc} 14 & -9 & 7 \\ 16 & -1 & 8
\end{array} \right)$

$BA = \left( \begin{array}{ccc} -3 & -1 & 1 \\ -10 & -5 & 0 \\ -4
& -3 & -2 \end{array} \right)$

$BB,\, BC, \, CA$ are all undefined.

$CB = \left( \begin{array}{cc} 3 & -5 \\ 4 & -5 \\ -5 & 7
\end{array} \right)$

$CC = \left( \begin{array}{ccc} 6 & -2 & 3 \\ 4 & 3 & 2 \\ 1 & -9
& 7 \end{array} \right)$

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