A Math Dilemma

Enough seriousness for the moment. This one is just for fun.

Okay, there is an error in here (obviously), but see if you can find it. (Note: The "^" symbol means "to the power of", so that "a^2" means "a to the power of 2" or "a squared".

Let a=b

Thus: a^2=ab

Add a^2 to both sides: a^2 + a^2 = a^2 + ab

Or: 2a^2 = a^2 + ab

Subtract 2ab from both sides: 2a^2 – 2ab = a^2 + ab – 2ab

Or: 2a^2 – 2ab = a^2 – ab

This can be factored to: 2(a^2 – ab) = 1(a^2 – ab)

If you divide both sides by a^2 – ab, you get: 2 = 1