Matrices And Determinants

Let A be a \(3 \times 3\) matrix and \(\operatorname{det}(A)=2\). If \(n=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots . .(\operatorname{adj} A))}_{2024-\text { times }}))\), then the remainder when \(n\) is divided by 9 is equal to __________.