The hadith of Sayyiduna Mu'awiyah bin al-Hakam al-Sulami (may Allah be pleased with him) has already passed, that he spoke behind the Prophet (peace and blessings be upon him) (in prayer) out of ignorance that speaking was forbidden, and yet the Prophet (peace and blessings be upon him) did not order him to perform the prostration of forgetfulness.
This is also narrated on the subject from Sayyiduna Ibn Abbas (may Allah be pleased with them both), and it is the view of Imam al-Sha'bi, Imam al-Nakha'i, Imam al-Zuhri and other imams (may Allah have mercy on them); and a weak hadith has also been narrated on this subject.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / Q3884
Salim bin Abdullah (may Allah have mercy on him) narrates that Jubayr bin Mut'im (may Allah be pleased with him) came to Ibn Umar (may Allah be pleased with them both) and said: O Abu Abd al-Rahman, what did Umar (may Allah be pleased with him) say about the one who leads people in prayer? Ibn Umar (may Allah be pleased with them both) said: He (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) said: "The imam suffices for those behind him. If the imam forgets, the prostrations of forgetfulness are obligatory upon the imam, and his followers will prostrate with him; and if one of the followers forgets, there is no prostration of forgetfulness upon him, and the imam will suffice for him."
This Abu al-Husayn is majhul (unknown), and al-Hakam bin Abdullah is da'if (weak). And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3884
Ibn Abi Uways and Isa bin Mina both narrate: Abd al-Rahman bin Abi al-Zinad (may Allah have mercy on him) narrated to us from his father, and he narrates from the jurists of the people of Madinah that the imam's sutrah is itself the sutrah of those following him, whether they are few or many, and he bears their burden.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 3885