WRONG. First of all, U CAN NOT EQUATE TWO DIFFERENT NUMBERS WITHOUT THE PRESENCE OF A VARIABLE.PERIOD
What u basically saying is
Let a=1 and b=1
so 1=1
1*1=1*1
1-1=1-1
0=0(derivation stops right here. bcoz it prooves the fact that a=b)
Since u have given the value at the begining to a and b then u r responsible to stop deriving it right at where it becomes Zero.
ie, (a+b)(a-b)=b(a-b)
(a+b)x0=bx0
0=0
Now, if i were to give u an equation a^2-b^2=ab-b^2 without giving any values to a and b then u can solve like (a+b)=b. U could use it like a general equation.
Now if i set the condition a=1, b=1 and give u to solve the same quation,a^2-b^2=ab-b^2, then u will endup with
0=0
In otherwards, u have to make a proper question for us to solve if there is something to solve (in this case nothing). But i respect ur curiosity.