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QUESTION

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

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ANSWER

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




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