It is narrated from Sayyiduna Ibn Umar (may Allah be pleased with them both), who reported that a man named Agharr (who belonged to the Muzaynah tribe and had the honor of being a companion of the Prophet, peace and blessings be upon him) was owed several wasqs of dates by a person from Banu Amr bin Awf, for which he had gone to demand payment several times. He says: I went to the service of the Prophet (peace and blessings be upon him) (and complained), so the Prophet (peace and blessings be upon him) sent Sayyiduna Abu Bakr Siddiq (may Allah be pleased with him) with me. He says: Whoever we met (on the way) would greet us with salam. Sayyiduna Abu Bakr (may Allah be pleased with him) said: Have you not noticed that people greet you first, so they receive the reward for initiating the greeting? If you initiate the salam, you will receive the reward. Sayyiduna Ibn Umar (may Allah be pleased with them both) used to narrate this from himself.
Benefits and Issues: ➊ The last phrase, "Ibn Umar radi Allahu anhuma..." can have two meanings: You initiate the greeting of peace (salam)... This is the personal statement of Sayyiduna Ibn Umar radi Allahu anhuma, which has been transmitted in the hadith as an insertion (idraj). Sayyiduna Ibn Umar radi Allahu anhuma used to practically demonstrate this and would always be the first to greet with salam, as has been mentioned in Hadith 982.
➋ From all the aforementioned narrations, it is understood that initiating the greeting of salam is superior and a means of attaining closeness to Allah Ta'ala.
Source: Fadlullah al-Ahad: Urdu Commentary on al-Adab al-Mufrad, Page: 984