I guess this is somewhat besides the point but checking if something can be multiplied by -1 is not great as a definition of subtraction. You'll typically want to use the additive inverse directly. I mean sure you can extend any commutative group into a module over the integers but you probably don't want to make this a hard requirement just to have subtraction.
Why would this be an issue? I'm under the impression that this is fine if we're operating with the standard addition operator and the standard field that everyone is used to working under. Isn't that the definition of the inverse? I understand that in different fields you have different operators but is that relevant here?
If you want to define the concept of subtraction then you probably don't want to assume you can multiply elements with an integer. Not that it can't be done but in general it will be a lot easier to define the additive inverse directly (if one exists).