Let A be a square matrix of order 3 with real entries such that \(|\mathrm{adj}\,A| = 49\). Then the possible values of \(|A|\) are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\pm 7\)
For a square matrix of order n, the determinant of the adjoint is
\( |\mathrm{adj}\,A| = |A|^{n-1} \)
With n = 3:
\( |A|^{2} = 49 \)
\( |A| = \pm 7 \)
Both signs are possible, because squaring removes the sign of \(|A|\).