For a \(2\times 2\) matrix A, if \(A(\mathrm{adj}\,A)=\begin{bmatrix}100 & 0\\ 0 & 100\end{bmatrix}\), then \(|A|\) is equal to:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100
For every square matrix, the adjoint result is
\(A(\mathrm{adj}\,A) = |A|\,I\)
For a 2 × 2 matrix:
\(|A|\,I = \begin{bmatrix}|A| & 0\\ 0 & |A|\end{bmatrix}\)
Comparing with the given matrix:
\(|A| = 100\)