and if neglecting it leads to estrangement, then shunning one’s brother for more than three days becomes unlawful, whereas three days or less is permissible. Obviously, a person will not boycott his brother without a cause, so the Prophet (peace and blessings be upon him) allowed a Muslim to avoid his brother for up to three days, because man is only human: something may remain in the heart and he may be unable either to offer the greeting or to return it. Hence the concession of three days or less.
Initiating the greeting should come from the younger to the elder, from the one who is walking to the one who is seated, and from the rider to the pedestrian, each according to his situation. The prescribed formula is to say as-salāmu ʿalaykum (peace be upon you) or as-salāmu ʿalayka; both are acceptable. The response is to say ʿalayka as-salām or wa ʿalaykum as-salām.
From this it becomes clear that the Prophet (peace and blessings be upon him) explained that giving the greeting and returning it are among the rights a Muslim owes his brother.
The ruling is that initiating the salām is a sunnah, while responding to it is obligatory: an individual obligation (farḍ ʿayn) upon the one addressed, and a collective obligation (farḍ kifāyah) when the greeting is directed to a group, for the response of any one of them suffices. Offering salām is a good deed, and whoever does so receives tenfold reward, for every good deed is multiplied ten times. Thus, if you greet your brother saying, “as-salāmu ʿalaykum,” you earn ten good deeds—a lasting recompense that you will find when you need it most.
We also know that if a person were told, “Each time you greet someone you will receive one dirham,” he would actively seek people out just to greet them for that single dirham, even though a dirham perishes and disappears. The reward and recompense, however, endure, and you will find them when you are in greatest need of them. May Allah deal with us and with you through His pardon and His bounty.