Let A be a non-singular square matrix of 2 × 2. Then, |adj A| is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(|A|\)
For a non-singular square matrix A of order n, the determinant of the adjoint is
\(|\mathrm{adj}\,A| = |A|^{n-1}\)
Here n = 2:
\(|\mathrm{adj}\,A| = |A|^{2-1} = |A|\)
A direct check:
\( \displaystyle A = \begin{bmatrix}a & b\\ c & d\end{bmatrix}, \quad \mathrm{adj}\,A = \begin{bmatrix}d & -b\\ -c & a\end{bmatrix} \)
Both determinants equal ad − bc.