Show that 0 is the only in R if and only if a^2 = 0 implies a = 0.
The Attempt at a Solution
So I'm not sure if I'm doing this right.
a^2 = a*a = 0. Therefore, either a or a is zero.
The reason i'm not sure about this is because i'm thinking about matrices, where matrix A^2 can equal zero while A doesn't equal zero.
Also, did the logic that I use only work if the original question considered the ring a domain?