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

Explanation

1. 01

   For order 3, $|\operatorname{adj} B| = |B|^2$ for any square matrix $B$. First $|\operatorname{adj} A| = 3^2 = 9$.

2. 02

   Apply it again with $B = \operatorname{adj} A$: $|\operatorname{adj}(\operatorname{adj} A)| = 9^2 = 81$.