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{\bf Question}

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

\vspace{.25in}

{\bf Answer}

$AA$ is undefined

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

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

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

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

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

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

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