Firstly, I apologise if this is in the wrong forum. I spent quite a bit of time looking through the different forums and this seems to be the one most appropriate.

Let $\displaystyle \alpha$ be such that $\displaystyle \alpha^3 = -1$ and $\displaystyle \alpha\neq-1$. Evaluate $\displaystyle (\alpha^2(\alpha - 1)^2)^{-1}$ without calculating explicitly the values of $\displaystyle \alpha$.

So far I have rewritten $\displaystyle (\alpha^2(\alpha - 1)^2)^{-1}$ as $\displaystyle (\alpha^2-\alpha+2)^{-1}$ by substituting $\displaystyle \alpha^3 = -1$ but am not sure how to proceed from here.