Muwatta Imam Malik (Riwayat Yahya)

It is narrated from Sayyiduna Zayd bin Aslam (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "The rider should greet the one who is walking, and when one man from a group greets, it is sufficient for all of them."

It is narrated from Muhammad bin Amr bin Ata (he says): I was sitting with Sayyiduna Abdullah bin Abbas, may Allah be pleased with them both, when a man from Yemen came and said: "As-salamu Alaikum wa Rahmatullahi wa Barakatuh," and added something more to it. In those days, Sayyiduna Ibn Abbas, may Allah be pleased with them both, had lost his eyesight. He said: "Who is this?" The people said: "This is the same man from Yemen who comes to you," and they informed him until Sayyiduna Ibn Abbas, may Allah be pleased with them both, recognized him. Sayyiduna Ibn Abbas, may Allah be pleased with them both, said: "The greeting ends at 'wa Barakatuh'; nothing should be added beyond this."

Yahya said: Imam Malik, may Allah have mercy on him, was asked: Should a man greet a woman with salam? He said: There is nothing wrong with greeting an old woman, but it is not good to greet a young woman.