Question

If $A$ is a square matrix of order 3 , then | adj $\left(\mathrm{adj}{A}^2\right)\mid$ is equal to

• A. $|A{|}^2$
• B. $|A{|}^4$
• C. $|A{|}^8$
• D. $|A{|}^{16}$

Answer 1

Answer: (C)

We know that,
$|\mathrm{adj}(\mathrm{adj}A)|=|A{|}^{(n-1{)}^2}$
$\left|\mathrm{adj}\left(\mathrm{adj}{A}^2\right)\right|={\left|A^2\right|}^{(3-1{)}^2}$
$={\left|A^2\right|}^2[\because n=3]$
$={\left|A^2\right|}^4=|A{|}^8$