1. Fasting on 1st day of Muharram highly recommended. Imam Ridha (pbuh) asks his companion, Ar Rayyan ibn Shabeeb – “Are you fasting?” He answers no. Imam then says: “Yabna Shabeeb! This is the day when Zakariyya at 75 years prayed to his Rabb (3:38) for a child. Allah accepts his dua and commands angel to go to his mihraab and announce the good news of a son Yahya (3:39). One who fasts and invokes Allah He will accept as the dua of Zakariyya”
2. It is mustahab to fast on the first nine days of the month.