Let A= [0, 1, 2; a, 0, 3; 1, c, 0], where a, c ∈ R. If A^3=A and the positive value of a belongs to the interval ( n-1, n ], where n ∈ N, then n is…

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