Question

If $A$ is a $3\times 3$ matrix such that $|A|=2,$ then $|\text{adj(adj(adj}A\left)\right)|$ is

• A. $512$
• B. $256$
• C. $64$
• D. $8$

Answer 1

The correct option is B $256$

We know that $|\text{adj}\left(\text{adj}A\right)|=|A{|}^{(n-1{)}^2}$
$\Rightarrow |\text{adj}\left(\text{adj}\right(\text{adj}A\left)\right)|=|\text{adj}A{|}^{(n-1{)}^2}=|A{|}^{(n-1{)}^3}$
As $n=3,$
$|\text{adj}\left(\text{adj}\right(\text{adj}A\left)\right)|=|A{|}^{(2{)}^3}=2^8=256$