Prove that if x2 = y2 then x=y or x = -y
The 12 Properties of numbers
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?