Let \(A = [a_{ij}]\) be a square matrix of order 3 with \(|A|= 2\) and let \(C = [C_{ij}]\), where \(C_{ij}\) = cofactor of \(a_{ij}\) in A. Then \(|C|\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
C is the matrix of cofactors, and the adjoint is its transpose: \(\mathrm{adj}\,A = C^T\). Since a matrix and its transpose have equal determinants,
\(|C| = |C^T| = |\mathrm{adj}\,A|\)
For a square matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). Here n = 3:
\(|C| = |A|^{2} = 2^2 = 4\)