Is there a report in the Sunnah regarding shaking hands and greeting those present in the gathering?

Question:
Is it from the Sunnah that when a person enters a gathering, he should greet them first and then shake hands with those in the gathering, or should he shake hands first and then greet, or should he greet and shake hands at the same time? And does he repeat the greeting with every handshake?

Answer:
Shaking hands is done when meeting or upon arriving from a journey. As for a person who enters upon people who are sitting, it is sufficient for him to greet them all by saying, "As-salamu alaykum wa rahmatullahi wa barakatuh," and then sit down. Is this sufficient? Yes.