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If $\mathrm{A}=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)$, then which one of the following is correct?
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Verified Answer
The correct answer is:
$A^{2}=-4 A$
$\mathrm{A}=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)$
$\mathrm{A}^{2}=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)$
$=\left(\begin{array}{cc}4+4 & -4-4 \\ -4-4 & 4+4\end{array}\right)=\left(\begin{array}{cc}8 & -8 \\ -8 & 8\end{array}\right)$
$=-4\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)=-4 \mathrm{~A}$
$\mathrm{A}^{2}=\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)$
$=\left(\begin{array}{cc}4+4 & -4-4 \\ -4-4 & 4+4\end{array}\right)=\left(\begin{array}{cc}8 & -8 \\ -8 & 8\end{array}\right)$
$=-4\left(\begin{array}{cc}-2 & 2 \\ 2 & -2\end{array}\right)=-4 \mathrm{~A}$
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