JEE Main 2020 (Online) 3rd September Evening ShiftQuestion 1
Let $A$ be a $3\times3$ matrix such that $\mathrm{adj}\,A=\begin{bmatrix}2&-1&1\\-1&0&2\\1&-2&-1\end{bmatrix}$ and $B=\mathrm{adj}(\mathrm{adj}\,A)$. If $|A|=\lambda$ and $|(B^{-1})^T|=\mu$, then the ordered pair, $(|\lambda|,\mu)$ is equal to :
Matrices
Solution
$\det(\mathrm{adj}A)=9$ (direct expansion) $=|A|^2$, so $|\lambda|=3$. $B=\mathrm{adj}(\mathrm{adj}A)$, $|B|=9^2=81$, so $|(B^{-1})^T|=\tfrac1{81}$. $(3,\tfrac1{81})$, option B.