Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
a + b = b
a = 0

Furthermore 
if a + b = b, 
       a = b, 
then 
   b + b = b, 
and 
      2b = b, 
which mean that 
       2 = 1.