Answer
It is forbidden to fast on the two days of Eid: Eid al-Fitr and Eid al-Adha; due to his saying, peace be upon him: "There is no fasting on two days: Eid al-Fitr and Eid al-Adha," in Sahih al-Bukhari 1: 400, and Sahih Muslim 2: 799. And from Umar, may Allah be pleased with him, he said: "These are two days that the Messenger of Allah, peace be upon him, forbade fasting on: the day of your breaking the fast, and the other is the day you eat from your sacrifices," in Sahih Muslim 2: 799. And from Abu Huraira, may Allah be pleased with him: "He forbade, peace be upon him, fasting on two days: the day of Eid al-Adha and the day of Eid al-Fitr," in Sahih Muslim 2: 799. And from Abu Sa'id, may Allah be pleased with him, he said, peace be upon him: "Fasting is not valid on two days: the day of Eid al-Adha and the day of Eid al-Fitr from Ramadan," in Sahih Muslim 2: 799, and in Musnad al-Mustakhraj 3: 217, and Musnad Abu Ya'la 2: 388. However, if a person begins to fast on the two Eids and breaks it, he is not required to make it up due to its invalidation. But if he vowed to fast it, it is valid, and if he breaks it, he must make it up. If he fasts it due to a vow, he is released from the obligation of the vow while it remains forbidden, as mentioned in Al-Hadiyyah Al-Ala'iyyah, p. 174.