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If $A=\left[\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right]$ then $A^2 \operatorname{Adj} A=$
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$-42 \mathrm{~A}$
$|\mathrm{A}|\left|\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right|$
$\begin{aligned} & =1-(-1-6)+3(2-9)+2(-4-3) \\ & =-7-21-14=-42\end{aligned}$
Now, $A^2 \operatorname{adj} A=A \cdot A \operatorname{adj} A=A|A|=-42$
$\begin{aligned} & =1-(-1-6)+3(2-9)+2(-4-3) \\ & =-7-21-14=-42\end{aligned}$
Now, $A^2 \operatorname{adj} A=A \cdot A \operatorname{adj} A=A|A|=-42$
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