If \(A = \begin{bmatrix}6 & 4\\ 5 & 3\end{bmatrix}\) and \(B = \mathrm{adj}(A)\), then \(|B|\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −2
\(|A| = 6 \times 3 - 4 \times 5 = 18 - 20 = -2\)
For a matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). Here n = 2:
\(|B| = |\mathrm{adj}\,A| = |A|^{1} = -2\)
A direct check:
\( \displaystyle B = \begin{bmatrix}3 & -4\\ -5 & 6\end{bmatrix} \)
\(|B| = 18 - 20 = -2\)