Given a matrix A of order 3 × 3. If $|A| = 3$ then the value of $\text{|A(adj A)|}$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 27
Given: $|A| = 3$
Let $A$ be a square matrix of order $n = 3$.
Property: $|A \cdot \text{adj}(A)| = |A|^n$
So, $|A \cdot \text{adj}(A)| = |A|^3$
Substitute $|A| = 3$:
$|A \cdot \text{adj}(A)| = 3^3 = 27$