Two numbers have their own reciprocals. What are they?

The two numbers that have their own reciprocals is 1 and - 1

The two numbers that are the same as their reciprocal are 1 and - 1.

The reciprocal of a/b is b/a.

The reciprocal of 1 is 1.

1 is nothing but 1/1. And if you flip the numerator and denominator, you get 1/1 which is 1.

The reciprocal of - 1 is - 1.

-1 is nothing but - 1/1. And if you flip the numerator and denominator, you get 1/-1 which is - 1.

The only two numbers that have their own reciprocals are 1 and - 1.