Let A be a non-singular matrix of order 3 and \(|A| = 15\), then \(|\mathrm{adj}\, A|\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 225
For a square matrix of order n, \(|\mathrm{adj}\, A| = |A|^{n-1}\). Here n = 3:
\(|\mathrm{adj}\, A| = |A|^{2}\)
\(= 15^2 = 225\)
The result comes from \(A(\mathrm{adj}\, A) = |A|\, I\): taking determinants, \(|A|\,|\mathrm{adj}\, A| = |A|^n\).
CBSE Applied Mathematics (Class XII):
Adjoint of a Matrix
