"Whoever treads on a path in search of Islamic knowledge, Allah will ease the way to Paradise for him. The angels will lower their wings, pleased with this seeker of knowledge, and everyone in the heavens and on earth will ask forgiveness for the knowledgeable person, even the fish in the deepest of waters will ask for his forgiveness”
[Abu Dawud, Ibn Majah, Tirmidhi # 2835-sahih hadith]
Giving Salaams to the Opposite Sex – Shaykh Muqbil ibn Haadee
The questioner asks about verbally giving the Salaams (to women).
Shaykh Muqbil: Verbally giving the Salaam, if she and he are safe from Fitnah, then there is no harm in him saying: As-Salaamu Alaykum. If he fears that the Salaam will lead to that which is after it from Fitnah, then no. As is said:
نظرة فإبتسامة فسلام فكلام فموعد فلقاء
A look; then a smile; then Salaams; then speaking; then (setting) an appointment; then a meeting
So if he does not fear Fitnah for himself and he does not fear for her then there is no harm in saying: As-Salaamu Alaykum. The wives of the Prophet (sallallaahu alayhi wa sallam) used to be greeted with Salaam. And Allaah’s Aid is sought.
Questioner: Does this apply to responding, as well, O Shaykh?
Questioner: Is responding to As-Salaamu Alaykum obligatory upon the woman?
Shaykh: Upon the woman, yes, she
is to respond. The same applies to her; if she fears Fitnah for herself
or that she will put the man to trial then she responds within herself.
Or she moves her lips with some sound (coming out) such that he does not
hear her. But if she does not fear (Fitnah) for herself or he is a
Mahram for her, then there is no harm in her saying: Wa Alaykum As-Salaam. However, if she fears the occurrence of Fitnah, then there is nothing equivalent to the safety of the heart.