Hello MarGab, Michael here. Thank you for your question - it’s a good one, and I’m sorry for the delay in responding. As you may know, grammar is theoretical and there are different ways of describing and categorising grammatical items. Here at Academic Marker, we agree with other grammarians that words such as ‘my’, ‘your’, ‘his’ and ‘her’ are possessive determiners rather than possessive adjectives.
In older grammar books, these words did used to be called possessive adjectives such as you said, but now they are more commonly described as being determiners, like quantifiers (some/many), articles (the/a) and demonstratives (this/these). This is because words such as ‘my’ and ‘your’ function more like determiners than they do adjectives. We can use possessive determiners in place of other determiners:
It is a book
It is that book
It is my book
We can also use these words in addition to adjectives:
It is an interesting book
It is this interesting book
It is your interesting book
I hope that helps