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QUESTION

Evaluate the product \textbf{AB} of the matrices

$$\textbf{A}=\left(\begin{array}{cc}1&-2\\-1&1\end{array}\right),\hspace{1cm}\textbf{B}=\left(\begin{array}{cc}2&-1\\3&1\end{array}\right).$$

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ANSWER


\textbf{AB} $=\left(\begin{array}{cc}1&-2\\-1&1\end{array}\right)
\left(\begin{array}{cc}2&-1\\3&1\end{array}\right)=
\left(\begin{array}{cc}2-6&-1-2\\-2+3&1+1\end{array}\right)=
\left(\begin{array}{cc}-4&-3\\1&2\end{array}\right)$




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