Here's the question:

An element $\displaystyle \displaystyle{a}$ in a non-trivial ring $\displaystyle R$ is callednilpotentif $\displaystyle a^k = 0$ for some integer $\displaystyle k \geq 1$. Prove that if a is nilpotent then a-1 has a multiplicative inverse. Give an example to illustrate this in $\displaystyle Z_{18}$.

I've absolutely no idea how to start this question. I'd be very grateful for any help