Example of wrong proof

Example of wrong proof
Find a mistake in the following chain of arguments, pretending to prove that 2=1

1)	Let a = b
2)	Multiply 1) by a a2 = ab
3)	Add a2 – 2ab to both parts of 2) a2 + a2 – 2ab = ab + a2 – 2ab
4)	3) could be simplified: 2a2 – 2ab = a2 – ab
5)	It is the same as 2(a2 – ab) = 1(a2 – ab)
6)	Reduce 5) by (a2 – ab). 2=1

Where is a mistake?
Mistake is in the 6^th step.
We can not divide by (a² – ab) because a²– ab = 0.
a = b, so a²– ab = 0.