1. The problem statement, all variables and given/known data Prove that if x2 = y2 then x=y or x = -y 2. Relevant equations The 12 Properties of numbers 3. The attempt at a solution I think I should do this case-wise: Case (a) if x=y then x2 = x*x=y*y=y2. Simple enough. Case (b) if x = -y then x2 = x*x=(-y)*(-y) = ... So what is left to show is that (-y)*(-y) = y*y which is where I am getting stuck. I was thinking of doing something like: (-y)(-y) = (-y)(-y)*1 = (-y)(-y) * [(-y)(-y)]*[(-y)(-y)]-1 ... but I don't see this going anywhere really. Any thoughts?