When $a, b > 0$ and $a = b$, how does $ab-a^2 = b^2 - a^2$?

Question

This may be very rudimentary, but nontheless,

when $a, b > 0$ and $a = b$, how does $ab-a^2 = b^2 - a^2$?

I know that: $a^2 = ab$, $a^2 = b^2$, and $b^2 = ab$

To give context, these are steps taken from the false proof for 1=2 (due to a step of dividing by 0 as part of the proof).

Answer 1

a=b, so they can be substituted for each other freely:

b^2-a^2=b^2-a^2

bb-a^2=b^2-a^2

ab-a^2=b^2-a^2.

a and b are just two names for the same thing.