If the imam recites a surah after Al-Fatihah in the last two rak'ahs out of forgetfulness, not intentionally, should he perform the prostration of forgetfulness (sujud al-sahw), and what is the ruling if he does prostrate?

Prostration of forgetfulness (sujud al-sahw) is not obligatory for someone who recites a surah after Al-Fatihah in the last two rak'ahs by mistake, because it is an addition of Quran. Ibn 'Umar used to recite Umm al-Quran (Al-Fatihah) and a surah in all four rak'ahs, and sometimes he would recite two or three surahs in a single rak'ah.