Where is wrong in this proof Suppose $a=b$.
Multiplying by $a$ on both sides gives $a^2 = ab$. Then we subtract $b^2$ on both sides, and get
$a^2-b^2 = ab-b^2$.
Obviously, $(a-b)(a+b) = b(a-b)$, so dividing by $a - b$, we find
$a+b = b$.
Now, suppose $a=b=1$. Then $1=2$ :)

By a simple example:
if( A = 0 ) A * 5 = A * 7 and by dividing by A we have 5 = 7.
Then we can dividing by A if A not equal to zero. 
