Let A be a non-singular square matrix of order 3 and \(|\mathrm{adj}\, A| = 5\) 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, \(|\mathrm{adj}\,A| = |A|^{n-1}\). Here n = 3:
\(|A|^2 = 5\)
\(|A| = \pm\sqrt{5}\)
Of these two values only \(\sqrt{5}\) is among the options.