If we allow division by zero any number
number can be made equal to any other
number.

Since a=b => a^2 - ab or a-b is zero.

a=b
a^2 = ab
a^2 - b^2 = ab-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

You cannot divide by a-b which is zero.