your proof just says 0=0=0 therefore 1=2 the real proof is as follows:
step 1: let a=b
step 2: square both sides,since a = b we can change one of them
a^2=ab
step 3: add a^2 to both sides
a^2 + a^2 = ab + a^2
step 4: reduce a^2 + a^2 to 2a^2
2a^2 = ab + a^2
step 5: subtract 2ab from both sides
2a^2 - 2ab = a^2 + ab - 2ab
step: 6 ab - 2ab is -ab
2a^2 - 2ab = a^2 - ab
step: 7 rewrite in factored form
2(a^2 - ab) = a^2 - ab
FINALLY factor out (a^2 - ab) from both sides.
we are left with 1=2
WTF?