It is twice singular, once masculine.
Twój kot - you is singular, cat is singular masculine
Twoje koty- you is singular , cats is plural not masculine personal
Twoi bracia- you is singular, brothers is plural masculine personal
Wasz kot - you is plural, cat is singular masc
Wasze koty - you plural, cats is plural not masculine personal
Wasi bracia -you plural, brothers is plural masculine personal
My understanding is that in Polish (as in Italian and French), the case and number of a possessive pronoun match that of the referent. So the easiest way to explain this is by writing "masculine singlar referent."
E.g., Mój pies je mięso = My dog eats meat. In this sentence, "Mój" is the possessive pronoun, pies is the referent (because Mój refers to pies), and mięso is the direct object. Since the referent is masculine singular, the possessive pronoun must also be masculine singular, regardless of whether the speaker is a man or a woman. Thus, even if I were a woman (which I'm not), I would still write "Mój pies je mięso" because the referent is masculine.
E.g., "moje psy jedzą mięsa" = my dogs eat meat. "Moye" is masculine plural because the referent, psy, is masculine plural.
This is confusing for people who only speak English because for English speakers, "my" does not inflect.
Everything is right, but:
- possessive pronoun or adjective has to match number, gender and case.
- 3rd person possessive pronouns do not change
- moje is plural not masculine personal (everything but masculine persons - dogs women, children, chairs(neuter), tables(masc.), wardrobes(fem.) )
- moi - is plural masculine personal
Just to clarify, for "Twój kot," I would describe Twój as a singular with a masculine singular referent. For "Wasz kot," I would describe Wasz as plural with a masculine singular impersonal referent. For "Twoje koty," I would say singular with a masculine plural referent. For "Wasze koty" I would say plural with a masculine plural impersonal referent.