$V$ is a matrix of order 3 such that $|\text{adj } V| = 7$. Which of these could be $|V|$?

$\pm\sqrt{7}$

The correct answer is Option (3) → $\pm\sqrt{7}$ ##

We know that, $|\text{adj } A| = |A|^{n-1}$ where $n$ is order of matrix.

Therefore, $|\text{adj } V| = |V|^{n-1}$

or, $7 = |V|^{3-1} \quad \text{here, } n = 3$

or, $7 = |V|^2$

or, $|V| = \pm\sqrt{7}$