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If $A(\operatorname{adj} A)=\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{array}\right]$, then $|\operatorname{adj} A|$ equals
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4
$A(\operatorname{adj} A)=\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{array}\right]=-2 I$ $A(\operatorname{adj} A)=|A| I \Rightarrow-2 I=|A| I$ $\Rightarrow \quad|A|=-2$ $\Rightarrow \quad|\operatorname{adj} A|=|A|^{n-1}, n=3$ $\Rightarrow \quad|\operatorname{adj} A|=|A|^{3-1}=|A|^{2}$ $|\operatorname{adj} A|=(-2)^{2}=4$
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