For a real number $\alpha$, if the system $\left[\begin{array}{lll}1 & \alpha & \alpha^2 \\ \alpha & 1 & \alpha \\ \alpha^2 & \alpha & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{r}1 \\ -1 \\ 1\end{array}\right]$ of linear equations, has infinitely many solutions, then $1+\alpha+\alpha^2=$