Matrices And Determinants

Let $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$$, where \(a, c \in \mathbb{R}\). If \(A^{3}=A\) and the positive value of \(a\) belongs to the interval \((n-1, n]\), where \(n \in \mathbb{N}\), then \(n\) is equal to ___________.