The "2=1?" Answer

The fallacy begins in line 5. While it's surely ok to subtract 2b from both sides, and also to factor out (a-b), you have to realize something very important while you do. It was assumed that a=b in the very beginning, right? That means that a-b = none other than ZERO. And since multiplying any muber by ZERO renders ZERO, all this proof is really prooving is that 0=0.