It depends upon whether the noun case is feminine, masculine, neuter, or plural (this appears under possessive pronoun lesson). In this case, "Hosen" is plural for pants, so it is "ihre". http://blogs.transparent.com/german/mein-dein-sein-ihr-etc-german-possessive-pronouns-in-the-nominative-case/
That is because all 3 answers mean her pants.
Ihre Hose. - Her pant(s). [since we do not use "pant" in English]
Die Hosen von ihr. - The pants of her. ["of" her dative format is ihr)
Ihre Hosen. - Her pants.
I think Hose is singular and Hosen is plural, it's just that 'pants' is both singular and plural in English.