every number equals its reciprocal

a = 1/b
b = 1/a
c = 1/ab
1/ab = 1/(1/b)(1/a)
1/(1/b)(1/a) = 1/(1/ab)
1/(1/ab) = ab
1/ab = ab

Now, COMPLETELY disregarding the original fractions assigned to A and B, let's begin anew:

a = 2
b = 2

1/2(2) = 2(2)

1/4 = 4
 

a = 1/b
b = 1/a
c = 1/ab
1/ab = 1/(1/b)(1/a)
1/(1/b)(1/a) = 1/(1/ab)
1/(1/ab) = ab <<<<WTF??? how did you get to the next step genius?
1/ab = ab

1/(1/ab) becomes ab, so really ab=ab not 1/ab reatrd. GTFO