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If $A=\left[\begin{array}{ccc}1 & 2 & -1 \\ -1 & 0 & 2 \\ 1 & 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}-3 & -2 & 4 \\ 2 & 2 & -1 \\ -2 & 0 & 3\end{array}\right]$, then $A^2=$
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The correct answer is:
$A+B$
$A=\left[\begin{array}{ccc}1 & 2 & -1 \\ -1 & 0 & 2 \\ 1 & 2 & 0\end{array}\right], B=\left[\begin{array}{ccc}-3 & -2 & 4 \\ 2 & 2 & -1 \\ -2 & 0 & 3\end{array}\right]$
$\begin{aligned} & A^2=\left[\begin{array}{ccc}-2 & 0 & 3 \\ 1 & 2 & 1 \\ -1 & 2 & 3\end{array}\right] \text { and } A+B=\left[\begin{array}{ccc}-2 & 0 & 3 \\ 1 & 2 & 1 \\ -1 & 2 & 3\end{array}\right] \\ & \therefore A^2=A+B .\end{aligned}$
$\begin{aligned} & A^2=\left[\begin{array}{ccc}-2 & 0 & 3 \\ 1 & 2 & 1 \\ -1 & 2 & 3\end{array}\right] \text { and } A+B=\left[\begin{array}{ccc}-2 & 0 & 3 \\ 1 & 2 & 1 \\ -1 & 2 & 3\end{array}\right] \\ & \therefore A^2=A+B .\end{aligned}$
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