Let A be a non-singular square matrix of order 3 and $|adj\, A| = 5$ then $|A|$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $±\sqrt{5}$
For a square matrix of order $n$,
$|\text{adj}A| = |A|^{\,n-1}$
Given $n=3$ and $|\text{adj}A|=5$,
$|A|^{\,3-1}=|A|^2=5$
$\Rightarrow |A|=\pm\sqrt{5}$
$|A|=\pm\sqrt{5}$