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QUESTION

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

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ANSWER


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




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