Let α be a root of the equation x^2+x+1=0 and the matrix A =1/(√ 3) [1, 1, 1; 1, α, α^2; 1, α^2, α^4], then the matrix A^31 is equal to:

Let $\displaystyle \alpha$ be a root of the equation $\displaystyle x^2+x+1=0$ and the matrix $\displaystyle \mathrm{A}=\frac{1}{\sqrt{3}}\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & \alpha & \alpha^2 \\ 1 & \alpha^2 & \alpha^4\end{array}\right]$, then the matrix $\displaystyle \mathrm{A}^{31}$ is equal to :