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QUESTION

Given that
$\textbf{C}=\left(\begin{array}{cc}-1&amp;2\\-2&amp;3\end{array}\right)$
evaluate $\textbf{CC}^T$.

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ANSWER

\begin{eqnarray*}
\textbf{CC}^T&amp;=&amp;\left(\begin{array}{cc}-1&amp;2\\-2&amp;3\end{array}\right)
\left(\begin{array}{cc}-1&amp;-2\\2&amp;3\end{array}\right)\\
&amp;=&amp;\left(\begin{array}{cc}-1(-1)+2(2)&amp;-1(-2)+2(3)\\-2(-1)+3(2)&amp;-2(-2)+3(3)\end{array}\right)\\
&amp;=&amp;\left(\begin{array}{cc}1+4&amp;2+6\\2+6&amp;4+9\end{array}\right)\\
&amp;=&amp;\left(\begin{array}{cc}5&amp;8\\8&amp;13\end{array}\right)
\end{eqnarray*}




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