There are 2 types of pronouns.
1st group. Some pronouns are declined like adjectives. These are: мой 'my', твой 'your (singular and informal)', наш 'our', ваш '(plural/formal)'. They change their form depending on the noun that follows them, and change their form depending on the gender and the case of the noun they modify:
- моё зе́ркало 'my mirror', (neuter, nominative case),
- моего́ зе́ркала 'of my mirror' (neuter, genitive case),
- моя́ кни́га 'my book' (feminine, nominative case),
- мое́й кни́ги 'of my book' (feminine, genitive case).
(N.B. In colloquial speech or dialects, this group includes a few ofter pronouns, the most popular being и́хний. Those are non-standard, and are usually avoided in written texts.)
2nd group. Other pronouns don't have a separate adjective-like form. Then, a genitive case of the pronoun is used: его́ 'his, its', её 'her', их 'their':
- его́ зе́ркало 'his mirror',
- его́ зе́ркала 'of his mirror',
- её кни́га 'her book',
- её кни́ги 'of her book'.
Those pronouns don't change their form depending on the case or gender of the thing they modify.
https://en.wikipedia.org/wiki/Russian_grammar this whole article is my little bible of russian declensions. There is a section for possesive pronouns: https://en.wikipedia.org/wiki/Russian_grammar#Possessive_adjectives_and_pronouns
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