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
Answer & explanation
Correct answer: option 4
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.
$∴|A^T| = 2\sqrt{2}$.