Let A be a $3\times 3$ matrix such that $adjA=\left[\begin{array}{ccc}2& -1& 1\\ -1& 0& 2\\ 1& -2& -1\end{array}\right]$ and $B=adj\left(adjA\right)$. If $\left|A\right|=\lambda$ and $\left|{\left(B^{-1}\right)}^{\top }\right|=\mu$, then the ordered pair $\left(\left|\lambda \right|, \mu \right)$ is equal to

• Correct answer
  A

  $\left(3, \frac{1}{81}\right)$
• B

  $\left(9, \frac{1}{9}\right)$
• C

  $\left(3, 81\right)$
• D

  $\left(9, \frac{1}{81}\right)$

Hence, the correct answer is option: 'A'.