If you greet a single person, do we say "As-salamu 'alayk"?

The questioner : Regarding the salam, some people are unsure what is correct. If you greet a group, I say: You greeted a single person, one individual. Do I say "As-salamu 'alaykum" or "As-salamu 'alayk"?

The Shaykh : As-salamu 'alayk. 'Alayk. 'Alayk.

The questioner : And if they are a group, 'alaykum. 'Alaykum, right?

The Shaykh : For a group, 'alaykum.

The questioner : And if a group responds to one person, do they say "Wa 'alayk as-salam" or "Wa 'alaykum"?

The Shaykh : So, 'alayk.

The questioner : And if the group...

The Shaykh : If the one being addressed is a single person, say "wa 'alayk" in the response and in the initial greeting. If they are a group, say "wa 'alaykum."

The questioner : Yes, in all cases, right.

The Shaykh : Hmm?

The questioner : In all cases, like that.

The Shaykh : Do not say "cases."

The questioner : I mean, if a single person greets, "wa 'alayk," and if a person greets...

The Shaykh : I am the one being addressed.