Allah Ta‘ala then said to Nabi Aadam (‘alaihis salaam), “This salaam and the greeting you heard from the angels will be your salaam and the salaam of your progeny.”
After Allah Ta‘ala created Nabi Aadam (‘alaihis salaam) and blew the rooh (soul) into him, Allah Ta‘ala said to him, “O Aadam! Go to that group of angels and greet them with salaam saying, ‘Assalaamu Alaikum.’ and thereafter listen to the reply that they give you, for that will be your greeting and the greeting of your progeny.”
Nabi Aadam (‘alaihis salaam) thus went to the angels and greeted them saying, “Assalaamu Alaikum.” Hearing the salaam, the angels replied saying, “Assalaamu Alaika Warahmatullah.” In other words, when the angels replied to the salaam of Nabi Aadam (‘alaihis salaam), they added the words “Warahmatullah”. (Saheeh Bukhaari #6227 and Sunan Tirmizi #3368)
Allah Ta‘ala then said to Nabi Aadam (‘alaihis salaam), “This salaam and the greeting you heard from the angels will be your salaam and the salaam of your progeny.”
The commentators of Hadith explain that the progeny mentioned in this Hadith refers to the ummah of Rasulullah (sallallahu ‘alaihi wasallam), as salaam is among the exclusive favors of Allah Ta‘ala upon the ummah of Rasulullah (sallallahu ‘alaihi wasallam). (Kashf-ul-Baari, Kitaab-ul-Istizaan pg.37)
Hence, Hazrat Abu Umaamah (radhiyallahu ‘anhu) reports that Rasulullah (sallallahu ‘alaihi wasallam) said, “Allah Ta‘ala made salaam the exclusive greeting of our ummah.” (Shu’ab-ul-Imaan #8798)
Similarly, in a lengthy narration reported by Hazrat Abu Zar (radhiyallahu ‘anhu), Rasulullah (sallallahu ‘alaihi wasallam) said, “I was the first Nabi to bring (to his ummah) the greeting of salaam.” (Saheeh Muslim #2473)
Likewise, in a Hadith reported by Hazrat Aaishah (radhiyallahu ‘anha), Rasulullah (sallallahu ‘alaihi wasallam) said, “The Jews are not jealous of you over anything as much as they are jealous of you over the exclusive favor you have been granted of the salaam and ameen.” (Sunan Ibnu Maajah #856)
Note: From these Ahaadith, we understand that the salaam is the exclusive favor of this ummah, and that no other ummah of any Nabi was granted this favor. Nevertheless, it should be borne in mind that the salaam being bestowed to Rasulullah (sallallahu ‘alaihi wasallam) as an exclusive favor for his his ummah does not negate the salaam being given to certain Ambiyaa (without their ummats). Therefore, in this Hadith, it is mentioned that Nabi Aadam (‘alaihis salaam) made salaam to the angels, and in certain other Ahaadith, it is mentioned that Nabi Musa (‘alaihis salaam) greeted Hazrat Khadir (‘alaihis salaam) with salaam upon meeting him.