I'm not 100% sure what you mean. but...
If you are saying "opposite numbers" as in say, 2 and -2
then the reciprocal of each number would still be opposite
2, -2 are opposite numbers
2 -----------------> 1/2
----reciprocal----
-2 -----------------> -1/2
(1/2) and (-1/2) are opposite numbers.
So the answer to your question in that regard would be "Yes, they are." If that is what you mean.