You can prove a negative. If I say Object A exists. I can ask you about object A. You might tell me several things about Object A since you can't show me an actual Object A. Some of those things might be impossible to exist together. If I could show how those things cannot coexist within any object, then so too, they cannot coexist in Object A. Therefore Object A cannot exist.

There are other ways one can prove a negative, but I am just illustrating that it can be done. I see a lot of people claim that you cannot prove a negative, which is a false statement.