$A$ is a square matrix of order 3 with $A(\operatorname{adj} A) = 5I$. What is $|\operatorname{adj} A|$?

Explanation

1. 01

   $A(\operatorname{adj} A) = |A|I$, so $|A| = 5$.

2. 02

   $|\operatorname{adj} A| = |A|^{n - 1} = 5^2 = 25$.