Let $A$ be a $3 \times 3$ matrix such that
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 $|\mathrm{A}|=\lambda$ and $\left|\left(\mathrm{B}^{-1}\right)^{\mathrm{T}}\right|=\mu$, then the ordered pair, $(|\lambda|, \mu)$ is equal to :
Correct Option: , 3
$\mathrm{C}=\operatorname{adj} \mathrm{A}=\left|\begin{array}{ccc}+2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1\end{array}\right|$
$|C|=|\operatorname{adj} A|=+2(0+4)+1 .(1-2)+1 .(2,4)$
$=+8-1+2$
$|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{2}=9=9$b
$\lambda=|\mathrm{A}|=\pm 3$
$|\lambda|=3$
$\mathrm{B}=\operatorname{adj} \mathrm{C}$
$|B|=|\operatorname{adj} C|=|C|^{2}=81$
$\left|\left(\mathrm{B}^{-1}\right)^{\mathrm{T}}\right|=|\mathrm{B}|^{-1}=\frac{1}{81}$
$(|\lambda|, \mu)=\left(3, \frac{1}{81}\right)$