Is it permissible for women to pray in their homes behind the Imam of the mosque, provided they can hear him and are aware of his movements, and does this apply to a woman praying in her private room?

If the women's prayer area is inside the mosque (whether on its upper or lower floor), their prayers are valid by scholarly consensus, even if they do not see the Imam or the congregants.

However, if they pray outside the mosque, such as in an adjacent house, there is a difference of opinion on the matter: Some scholars hold that their prayer is valid if the rows are connected, even if they do not see the Imam, while others prohibit it. Sheikh Ibn Uthaymeen is of the view that the prayer is valid if the rows are connected and there is no space within the mosque; otherwise, it is not. The more cautious approach for women in this situation is to pray in another mosque that can accommodate them, or for one of them to lead them in prayer, because it is an act of worship whose validity is disputed. The Permanent Committee issued a fatwa stating that prayer outside the mosque is not valid unless the rows are connected and it is possible to follow by sight and hear the voice.