It is not farz but highly recommended (with great emphasis). Greeting one another with al-Salamu ‘Alaykum (peace be to you) and responding with Wa ‘Alaykum al-Salam (and peace be to you) is part of Sunnah which was instituted by Prophet Muhammad (sws) in his Ummah alongside other Customs and Etiquettes (Whole list of Sunnah: Discussion 49769 • Reply 49794).

Such customs (adaab) given as Sunnah are not obligatory but if they are left intentionally, they will reap a minor sin.

Please refer to the video below from 32:14 to 34:18

For Importance of Sunnah of Salam, please refer to the video below from 8:46 to 9:53