1. The problem statement, all variables and given/known data Show that 0 is the only in R if and only if a^2 = 0 implies a = 0. 2. Relevant equations none 3. 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?