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