If A is square matrix of order 3 and A.(Adj.(A)) = 10I, then the value of \(\displaystyle\frac{1}{25}\left|\mathrm{Adj.}(A)\right|\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4
For every square matrix, \(A(\mathrm{adj}\,A) = |A|\,I\). Comparing with \(A(\mathrm{adj}\,A) = 10I\):
\(|A| = 10\)
For a matrix of order n, \(|\mathrm{adj}\,A| = |A|^{n-1}\). Here n = 3:
\(|\mathrm{adj}\,A| = 10^2 = 100\)
\( \displaystyle \frac{1}{25}\left|\mathrm{adj}\,A\right| = \frac{100}{25} = 4 \)