Women covering their hair at home

It is compulsory upon a woman to cover her entire body and hair with the exception of her hands till her wrists before non-mahrams (strange men).

While in the home, at times, there will be other people present in the home as well e.g. the servants or other family members with whom observing purdah is compulsory. If non-mahrams are present in the home, then through a woman not covering her hair, she will be exposing her satar before them. Hence, this will be impermissible.

If there are no non-mahrams present in the home, then though it will be permissible for a woman to expose her hair, covering her hair will be better so that she is not deprived of the company of the Malaaikah.

And Allah Ta'ala (الله تعالى) knows best.