$V$ is a matrix of order 3 such that $|\text{adj } V| = 7$. Which of these could be $|V|$?
Answer & explanation
Correct answer: option 3
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, $|V| = \pm\sqrt{7}$