Let A be a non-singular square matrix of order n with |adj A| = 64 and |A| = 4, then ‘n’ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
For a square matrix of order n, the determinant of the adjoint is
\(|\mathrm{adj}\,A| = |A|^{n-1}\)
Putting the given values:
\(4^{n-1} = 64\)
\(4^{n-1} = 4^3\)
\(n - 1 = 3\)
\(n = 4\)
Tip: Remember \(|\mathrm{adj}\,A| = |A|^{n-1}\), not \(|A|^n\); using \(|A|^n\) here would give n = 3, Option (1).