If $A$ is a square matrix of order 3 such that the value of $|\text{adj } A| = 8$, then the value of $|A^T|$ is

$2\sqrt{2}$

The correct answer is Option (4) → $2\sqrt{2}$ ##

$|\text{adj } A| = |A|^{n-1}$

where, $n$ is the order of square matrix A.

Given, $|\text{adj } A| = 8$

$|A|^{n-1} = 8$

$\Rightarrow|A|^{3-1} = 8$

$\Rightarrow |A|^2 = 8$

$\Rightarrow|A| = 2\sqrt{2}$

Also, determinant of a matrix and its transpose has same values.

$∴|A^T| = 2\sqrt{2}$.