Question

If A is a Square matrix of order 3, then |Adj(AdjA${}^2$)|=

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

Answer 1

Answer: (C)

$A$${}^8$

We know that.

$|Adj\left(AdjA\right)|={|A|}^{{(n-1)}^2}$

$n\to$ order of the square matrix.

$\Rightarrow |Adj\left({AdjA}^2\right)|={{|A}^2|}^{{(n-1)}^2}$

Given $n=3$

$\Rightarrow |Adj\left({AdjA}^2\right)|={{|A}^2|}^{{\left(2\right)}^2}$

$=|A{|}^8$

$\Rightarrow |Adj\left({AdjA}^2\right)|=|A{|}^8$

Hence, $A^8$ is the correct answer.