Let $A$ be a $3 \times 3$ matrix such that $\operatorname{adj} A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1\end{array}\right]$ and
$B=\operatorname{adj}(\operatorname{adj} A)$. If $|A|=\lambda$ and $\left|\left(B^{-1}\right)^{T}\right|=\mu$, then the ordered pair, $(|\lambda|, \mu)$ is equal to :
Correct Option: 1
$|\operatorname{adj} A|=|A|^{2}=9 \quad\left[\because|\operatorname{adj} A|=|A|^{n-1}\right]$
$\Rightarrow|A|=\pm 3=\lambda \Rightarrow|\lambda|=3$
$\Rightarrow|B|=|\operatorname{adj} A|^{2}=81$
$\mu=\left|\left(B^{-1}\right)^{T}\right|=\left|B^{-1}\right|=|B|^{-1}=\frac{1}{|B|}=\frac{1}{81}$
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