If \(A=\begin{bmatrix}a & 0 & 0\\0 & a & 0\\0 & 0 & a\end{bmatrix}, a \ne 0\) then |adj A| is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(a^6\)
A is a diagonal matrix, so its determinant is the product of the diagonal entries:
\(|A| = a \cdot a \cdot a = a^3\)
For a square matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). With n = 3:
\(|\mathrm{adj}\,A| = |A|^2 = \left(a^3\right)^2 = a^6\)