How do you know that it is my mother and not his mother?
It's kinda implied.
You would use something like '...do bytu jeho matky.' to stress that it's his mother. Otherwise, I would assume you talk about your own mother.
Thanks for the explanation. Is this a general assumption, that the unspecified person is related to the speaker unless it's explicitely stated otherwise?
I'd say so.
I see. Thanks!
Which case is matčina? shouldnt it be genitive, matky?
matka rod: ž. jednotné číslo množné číslo 1. pád matka matky 2. pád matky matek 3. pád matce matkám 4. pád matku matky 5. pád matko matky 6. pád matce matkách 7. pád matkou matkami
It's an adjective "matčin" Wiktionary link
In this sentence, "bytu" is genitive? It is influenced by prep "do"?
yes
It should be taken without "my".. it's not specified