If A is a square matrix of order 3 and |A| = 5, then the value of |A adj A|, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 125
For a square matrix of order n, \(A\,(\mathrm{adj}\,A) = |A|\,I\). Here n = 3, so
\( A\,(\mathrm{adj}\,A) = 5I \)
Taking determinants, with \(|kI| = k^n\) for the identity matrix of order n:
\( |A\,\mathrm{adj}\,A| = |5I| = 5^3 = 125 \)
Equivalently, \(|\mathrm{adj}\,A| = |A|^{n-1} = 5^2 = 25\), and \(|A|\,|\mathrm{adj}\,A| = 5 \times 25 = 125\).