You can handle this problem using something of a dirty trick. From the real numbers, we have the following formula:
This suggests that we try to show that . Try carrying it out to see what you get.
Here's the question:
An element in a non-trivial ring is called nilpotent if for some integer . Prove that if a is nilpotent then a-1 has a multiplicative inverse. Give an example to illustrate this in .
I've absolutely no idea how to start this question. I'd be very grateful for any help