The Prophet ﷺ used to give the salam to his right and to his left, saying, "Peace be upon you and the mercy of Allah, peace be upon you and the mercy of Allah."
حدثنا بندار محمد بن بشار حدثنا عبد الرحمن بن مهدي حدثنا سفيان عن أبي إسحق عن أبي الأحوص
عن النبي ﷺ أنه كان يسلم عن يمينه وعن يساره السلام عليكم ورحمة الله السلام عليكم ورحمة الله
[Sahih]. Abu Dawud (996), Ibn Majah (914), and Nasai (3/63) also narrated it, as did Ahmad (1/408), and Ibn Khuzayma graded it sahih (1323), from the hadith of Abu Ishaq with the same wording. He explicitly stated that he heard it directly, as recorded by Ahmad (1/408, no. 728) and Ibn Hibban (al-Ihsan, 1990). The hadith has many corroborating narrations.There are also reports on this subject from Saad bin Abu Waqqas [Muslim, 582], Ibn Umar [Nasai, 1321, and Bayhaqi, 2/178], Jabir bin Samura [Muslim, 431], Bara [Bayhaqi, 2/177, and Daraqutni, 3/357, no. 1335], Abu Saeed [Ibn Majah, 916], Waail bin Hajar [Abu Dawud, 997], Adi bin Umayra [Ahmad, 4/192,193, and Ibn Khuzayma graded it sahih, 650], and Jabir bin Abdullah [Aqeeli in al-Duafa, 1/177,178].