It is narrated from Sayyiduna Jabir (may Allah be pleased with him), he says: When two people walking meet together, the one who initiates the greeting of peace is superior.
Hadith Referenceالادب المفرد / كتاب السلام / 994
Hadith Gradingالألبانی:صحيح
Hadith Takhrij«صحيح : صحيح ابن حبان (ابن بلبان) ، ح : 498.»
Explanation & Benefits
Shaykh Maulana Usman Muneeb
Benefits and Issues: ➊ In the aforementioned ahadith, the etiquettes of offering salam (greeting of peace) have been mentioned. Thus, every person who possesses any kind of superiority or distinction should initiate the salam; however, those who are fewer in number should begin the salam to those who are greater in number. ➋ If one person from among a group or congregation offers salam, it will suffice on behalf of all. Similarly, if one person responds, that will also be sufficient. ➌ If both parties are riding or both are walking, then the one who initiates the salam is superior. Furthermore, in the other aforementioned scenarios, if the other party offers the salam, that is also permissible.
Source: Fadlullah al-Ahad: Urdu Commentary on al-Adab al-Mufrad, Page: 994