If A is a square matrix of order 3 and |A| = 5, then |adj(adj A)| is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - 625
$\text{For an } n \times n \text{ matrix: } |\text{adj } A| = |A|^{n-1}$
$|\text{adj}(\text{adj } A)| = |\text{adj } A|^{n-1}$
$n = 3,\;\; |A| = 5$
$|\text{adj } A| = 5^{3-1} = 5^2 = 25$
$|\text{adj}(\text{adj } A)| = 25^{3-1} = 25^2 = 625$
$|\text{adj}(\text{adj } A)| = 625$