If \(A = \begin{bmatrix}2 & 5\\ 1 & x\end{bmatrix}\) and \(|\mathrm{adj}\,A| = 7\), then the value of x is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6
For a square matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). For order 2 the power is 1, so \(|\mathrm{adj}\,A| = |A|\).
\(|A| = 2x - 5\)
So
\(2x - 5 = 7\)
\(x = 6\)
Check: \(\mathrm{adj}\,A = \begin{bmatrix}6 & -5\\ -1 & 2\end{bmatrix}\), whose determinant is \(12 - 5 = 7\).