A note that it is not part of the Sunnah to say "As-salamu alaykum" to each individual present in the gathering.
Machine translationRead the Arabic original
The Shaykh : To one of the people sitting there, a greeting? Is this a custom of some people that you were influenced by?
The questioner : Shouldn't this be taken from the hadith regarding shaking hands?
The Shaykh : How?
The questioner : From the hadiths regarding shaking hands?
The Shaykh : I am not speaking about shaking hands, I am saying!
The questioner : Ah, meaning the phrase "As-salamu alaykum" to each person?
The Shaykh : Yes, as for shaking hands, you have done well; perhaps it is an expiation for what you innovated!
The questioner : Yes, that is correct, because we do not know of any basis in the Sunnah for the phrase "As-salamu alaykum" to each person in the group.
The Shaykh : This is what I wanted you to remember, may Allah bless you.
The questioner : May Allah reward you with good, may Allah reward you.
The questioner : Shouldn't this be taken from the hadith regarding shaking hands?
The Shaykh : How?
The questioner : From the hadiths regarding shaking hands?
The Shaykh : I am not speaking about shaking hands, I am saying!
The questioner : Ah, meaning the phrase "As-salamu alaykum" to each person?
The Shaykh : Yes, as for shaking hands, you have done well; perhaps it is an expiation for what you innovated!
The questioner : Yes, that is correct, because we do not know of any basis in the Sunnah for the phrase "As-salamu alaykum" to each person in the group.
The Shaykh : This is what I wanted you to remember, may Allah bless you.
The questioner : May Allah reward you with good, may Allah reward you.