"Czyje" is singular neuter or plural (but not the masculine personal plural) for "whose". "Kogo" is genitive or accusative for "who", and usually "whom" would be an even better equivalent:

Kogo zaprosiłeś? - Whom did you invite?

Do kogo należy ten pies? - To whom does this dog belong?

It is also a very widespread mistake among natives, to use 'kogo' when a form of 'czyj' should be used. If you really encountered 'kogo' as 'whose' in this course, frankly, I would be really surprised.

In (Nom.) singular, "czyj" is masculine, "czyje" is neuter, and "czyja" is feminine. In plural, "czyi" is masculine personal, and "czyje" is everything else.