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QUESTION

Evaluate the product \textbf{AB} of the matrices

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

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ANSWER

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




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