If A is a skew-symmetric matrix of order 5, then |adj A| is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
A is skew-symmetric, so \(A^T = -A\). Taking determinants, with order 5:
\(|A| = |A^T| = |-A|\)
\(= (-1)^5|A| = -|A|\)
\(2|A| = 0,\quad |A| = 0\)
For a square matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). With n = 5:
\(|\mathrm{adj}\,A| = 0^4 = 0\)