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QUESTION

Evaluate the product \textbf{AB} of the matrices

$$\textbf{A}=\left(\begin{array}{cc}2&amp;-1\\-2&amp;0\\1&amp;1\end{array}\right),
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\textbf{B}=\left(\begin{array}{ccc}1&amp;-2&amp;2\\2&amp;0&amp;1\end{array}\right).$$

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ANSWER

\begin{eqnarray*}
\textbf{AB}&amp;=&amp;\left(\begin{array}{cc}2&amp;-1\\-2&amp;0\\1&amp;1\end{array}\right)
\left(\begin{array}{ccc}1&amp;-2&amp;1\\2&amp;0&amp;1\end{array}\right)\\&amp;=&amp;
\left(\begin{array}{ccc}2(1)-1(2)&amp;2(-2)-1(0)&amp;2(1)-1(1)\\
-2(1)+0&amp;-2(-2)+0&amp;-2(1)+0\\1(1)+1(2)&amp;1(-2)+0&amp;1(1)+1(1)\end{array}\right)\\
&amp;=&amp;\left(\begin{array}{ccc}0&amp;-4&amp;1\\-2&amp;4&amp;-2\\3&amp;-2&amp;2\end{array}\right)
\end{eqnarray*}




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