The last step, the division by (a-b).a=b for some a, some b
a+a=a+b (add a to both sides)
2a-2b=a+b-2b (subtract 2b from oth sides)
2 = 1 (divide by a-b)
One step here is wrong, or so the teacher says. Which one is it?
You said a=b at the beginning. If that is so, then a-b = 0.
Hence, since you cannot divide by zero, then the last step is wrong.