Must the Imam perform the prostration of forgetfulness (Sujud Al-Sahw) if he makes a mistake in the Sunnah prayer (Eid), and what should he do if he does not prostrate?

All that is obligatory in other prayers is obligatory in the Eid prayer. Scholars have differed concerning the ruling on Eid prayer: The Hanafis believe it is an individual obligation, while the Shafi'is and Malikis believe it is a confirmed Sunnah. The Hanbalis believe it is a communal obligation (fard kifayah). The preponderant opinion is that of the majority, which states it is a confirmed Sunnah. As for the imam's error in the Eid prayer, it is like his error in other prayers. It is not prescribed for the imam to perform the prostration of forgetfulness (sujud as-sahw) or to make up the Eid prayer after its time has passed. He must repent to Allah if he intentionally omitted the prostration.