Find out the FALLACY

                Find out the fallacy

      Here I'm going to prove that 1 = 2 

Let's assume.        a = b ..........(1)

Then, evidently,   ab=b²

Subtracting b² from both sides, we get,

           ab - b² = a² - b², Now factoring we get

b(a - b) = (a +b) (a - b), dividing  both sides by

 ( a-b ), we get,  b = a + b, But according to equation (1) a = b

Therefore b = 2b

Dividing both sides by 'b', we have the required result  1= 2

This is impossible, right ??

Find out the FALLACY.