If \(A=\begin{bmatrix}a&a&a\\0&a&a\\0&0&a\end{bmatrix}\), then \(|\mathrm{adj}\, A|\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(a^6\)
A is upper triangular, 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, \(|\mathrm{adj}\,A| = |A|^{n-1}\). Here n = 3:
\(|\mathrm{adj}\,A| = |A|^2 = (a^3)^2 = a^6\)