´It was narrated that Wasi' bin Habban said:` "I said to Ibn 'Umar: "Tell me about the prayer of the Messenger of Allah (ﷺ); how was it?" He mentioned the takbir and he mentioned: As-salamu 'alaykum wa rahmatullah (peace be upon you and the mercy of Allah) to his right and: As-salamu 'alaykum (peace be upon you) to his left."
Hadith Referenceسنن نسائي / كتاب السهو / 1322
Hadith Gradingالألبانی:حسن صحيح | زبیر علی زئی:إسناده صحيح
Hadith Takhrij«تفرد بہ النسائي، أنظر ما قبلہ (حسن صحیح)»
Brief Explanation
1؎ : The purpose of mentioning this hadith is to show that, out of respect for those on the right side, the Prophet (sallallahu alayhi wa sallam) would add «ورحمۃاللہ» when turning his greeting of peace (salam) to the right, and on the left side he would suffice with only «السلام عليكم». In the previous narration, saying «ورحمۃاللہ» on the left side as well is mentioned, and this is the practice. Perhaps the Prophet (sallallahu alayhi wa sallam) would occasionally omit it.