JEE Main 2020 (Online) 9th January Morning ShiftQuestion 1
If the matrices $A=\begin{bmatrix}1&1&2\\1&3&4\\1&-1&3\end{bmatrix}$, $B=\mathrm{adj}\,A$ and $C=3A$, then $\frac{|\mathrm{adj}\,B|}{|C|}$ is equal to :
Determinant
Solution
$|A|=1(9+4)-1(3-4)+2(-1-3)=6$. $B=\operatorname{adj}A$, so $|B|=|A|^2$, $|\operatorname{adj}B|=|B|^2=|A|^4=1296$. $|C|=|3A|=27\cdot6=162$. Ratio $=1296/162=8$. Option (B).