2=1

I remembered this old problem solving technique from my 2nd year high school math teacher and found it quite amusing again. This is how he proved that 2 = 1!

Let a = b

Then a^2 = ab

Add a^2 to both sides of the equation,
Then a^2 + a^2 = a^2 + ab
Then 2a^2 = a^2 + ab

Subtract 2ab from both sides of the equation
Then 2a^2 -2ab = a^2+ ab - 2ab
Then 2a^2 -2ab = a^2 - ab

Factor out 2 from the left side of the equation
Then 2 (a^2-ab) = a^2-ab

Divide (a^2-ab) from both sides of the equation
Then 2 = 1!

Find the fallacy of this algebraic solution.