Find the flaw in this.. (solving a=b)

[nahya^^]

I came across this problem and am VERY perplexed. So I guess 2 does equal 1.

Let a=b

(a^2) = ab
(a^2) + a^2 = (a^2) + ab
2(a^2) = (a^2) + ab
2(a^2) - 2ab = (a^2) - ab
{2[(a^2) - ab]} / [(a^2) - ab] = [(a^2) - ab] / [(a^2) - ab]
2 = 1

My notion is that in the process of dividing the equation by (a^2) - ab is the flaw.

On the left side of the equation of the 4th step (1st step being (a^2) = ab), it would seem that there are no flaws if there wasn't the coefficient 2 for ab. so (a^2) - ab will cancel out on both sides and 2 and 1 are left.

I also think that there are no flaws, it's just that you can't derive numerical answers from an equation composed of variables and nothing else. Therefore the actual answer to a=b is no solution.

What do you guys think?

P.S.: How do you guys make the number 2 in A^2 a superscript?
P.P.S.: Whoops. Sorry, guys, I forgot to type the dividing part.