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
 

>> 1

c = 1 (when a!= 0; a * (1/a) = 1)

and you can not completely disregard original assumptions. a and b must be reciprocial to one another.