(which would prove nothing anyway, as "a = b" is a first condition, and also a result of the prove, so it has no any sense at all)
But as I said that calculations don't prove anything. They just go like that:
a = b
a * b = a * a
(a * b) - (b * b) = (a * a) - (b * b)
a * (a - b) = b * (a - b)
a = b
How does it prove that a = b?