Question

If A is a square matrix of order $3$, then $\left|\begin{array}{c}\left(AdjA\right)\end{array}\right|=$

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

Answer 1

Answer: (C)

$|A{|}^2$

We know that,

$|adjA|=|A{|}^{n-1}$

Where $n$ is the order of matrix $A$

Here, $n=3$

$|adjA|=|A{|}^{3-1}$

$\Rightarrow$ $|adjA|=|A{|}^2$