If you notice that the more money you have, the less money your brother has, you’ve discovered an inverse relationship: when your bank account increases, his decreases.
The word inverse traces back to the Latin inversus, from the past participle of invertere, meaning “turn upside down" or "turn about.” It’s a good word to use when you need to describe one of those topsy-turvy relationships in which when one thing goes up, the other goes down. It can also be used in a broader sense to mean “opposite.” You’ve probably heard someone begin a sentence by saying, “And the inverse was true for so and so . . .” That just means the opposite was true.