Given a matrix A of order 3 × 3. If \(|A| = 3\) then the value of \(|A(\mathrm{adj}\,A)|\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 27
For any square matrix, the adjoint property gives
\(A(\mathrm{adj}\,A) = |A|\,I = 3I\)
For a matrix of order n, \(|kI| = k^n\). Here n = 3:
\(|A(\mathrm{adj}\,A)| = |3I| = 3^3 = 27\)
Tip: Multiplying a 3 × 3 matrix by k multiplies every row by k, so \(|kA| = k^3|A|\), not \(k|A|\). Taking \(|3I|\) as 3 gives the wrong Option (1).