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QUESTION

Evaluate the product \textbf{AB} of the matrices $$\textbf{A}=
\left(\begin{array}{cc}-2&0\\1&1\\2&-2\end{array}\right),
\hspace{1cm} \textbf{B}
=\left(\begin{array}{ccc}1&2&-2\\-1&0&1\end{array}\right).$$

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ANSWER


\begin{eqnarray*}
\textbf{AB}&=&
\left(\begin{array}{cc}-2&0\\1&1\\2&-2\end{array}\right)
\left(\begin{array}{ccc}1&2&-2\\-1&0&1\end{array}\right)\\
&=&\left(\begin{array}{ccc}-2+0&-4+0&4+0\\1-1&2+0&-2+1\\2+2&4+0&-4-2\end{array}\right)\\
&=&\left(\begin{array}{ccc}-2&-4&4\\0&2&-1\\4&4&-6\end{array}\right)
\end{eqnarray*}




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