The Messenger of Allah ﷺ said, "The imam is appointed only to be followed. So when he says the takbir, say the takbir. When he recites, listen in silence. When he says 'not of those who have earned Your anger, nor of those who have gone astray' [Fatihah 1:7], say 'Ameen.' When he bows, bow. When he says, 'Allah hears the one who praises Him,' say, 'O Allah, our Lord, to You belongs all praise.' When he prostrates, prostrate. And if he prays sitting down, then all of you pray sitting down."
حدثنا أبو بكر بن أبي شيبة حدثنا أبو خالد الأحمر عن ابن عجلان عن زيد بن أسلم عن أبي صالح
قال رسول الله ﷺ إنما جعل الإمام ليؤتم به فإذا كبر فكبروا وإذا قرأ فأنصتوا وإذا قال {غير المغضوب عليهم ولا الضالين} فقولوا آمين وإذا ركع فاركعوا وإذا قال سمع الله لمن حمده فقولوا اللهم ربنا ولك الحمد وإذا سجد فاسجدوا وإذا صلى جالسا فصلوا جلوسا أجمعين
Sourcing, sahih. Abu Dawud reported it in the Book of Prayer, chapter on the imam praying while sitting, hadith no. 604, from the hadith of Abu Khalid, with this wording. Imam Muslim graded it sahih, and it has a corroborating narration in his Sahih. The hadith does not indicate a prohibition on reciting Fatihah behind the imam. See hadith no. 838.