Mathematics: Prove of 1=2

When I was class nine. Someone told me to prove 2=1. That's mean, if someone give 1, he can get 2. That time I gave him this prove,

  We know,
                  0=0
              ▶ 1*0=2*0

              ▶ 1=2 [divided by 0 and
                         proved]

That time he couldn't get the mistake of the prove. The mistake is, we can't divide 0 by anything.  So, here we can't divide 0 by 0.

Here have another prove of that. But, normally anyone can't get mistake of these equation. Here the prove...

If a=b,

We can write , a^2 = ab and a^2-b^2=0.

SO,
      a^2-b^2=a^2-ab
   ▶(a+b)(a-b)=a (a-b)
   ▶a+b=a
   ▶2a=b
   ▶2 = 1

So, 2 = 1 is proved......