Let A be a 3 × 3 matrix and det (A)=2. If n= det ( adj ( adj (… ….( adj A))))_2024- times, then the remainder when n is divided by 9 is equal to ____.

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