Saying Amin is recommended for those who are not praying (when reciting Al-Fatihah) and is strongly recommended for those who are praying, whether alone or behind the Imam. The two Sahihs recorded that the Messenger of Allah said,
When the Imam says, ‘Amin’, they say, ‘Amin’, because whoever says, ‘Amin’ with the angels, his previous sins will be forgiven.
Muslims recorded that the Messenger of Allah said,
When any of you says in the prayer, ‘Amin’ and the angels in the heaven say, ‘Amin’, in unison, his previous sins will be forgiven.
It is said that the Hadith (Hadith are the collections of the reports purporting to quote what the Islamic prophet Muhammad said verbatim on any matter. Hadiths are second only to the Quran in developing Islamic jurisprudence, and as regarded important tools for understanding the Quran and commentaries or tafsir on it) talks about both the angels and the Muslims saying Amin at the same time. The Hadith also refers to when the Amins said by the angels and the Muslims are equally sincere (thus bringing about forgiveness).
Further, Bilal narrated that he said,
O Messenger of Allah! Do not finish saying Amin before I can join you. This was recorded by Abu Dawud.
Source: Amin- Abdul Wadud Amin