ASSALAM O ALAIKUM!
Saying โAmeenโ after Surah Al-Fatiha is righteous (or Mustahab) in Islam. โAmeenโ can be examplified with โYaseenโ.
It means โO Allah! Undertake my grantsโ.
Righteousness (Mustahab) of saying โAmeenโ is backed by the Hadithย of Wail Bin Hajar (r.a.) narrated by Masnad Ahmad, Abu Dawood & Trimidhi (r.a.) According to him, โI heard Muhammad (sal allah ho alaihi wasallim) saying โAmeen โ after reciting Surah Al Fatiha.
Our wise men say that one who is not in Salah should also say โAmeenโ after the Imam recites Surah Al Fatiha. But one who is in Salah has more compulsion in saying โAmeenโ.
Abu Hurera (r.a.) narrated that Muhammad (sal allah ho alaihi wasallim) said, โWhen your Imam says Ameen, you should also say the same. Whose โAmeenโ concides with Ameen of Angels, will be forgiven!โ (SAHEHEEN)
This means that one a man & angels happen to say โAmeenโ simultaneously, the sins of that man are forgiven by the Lord!
Hazrat Ibn e Abbas (r.a.) said to Muhammad (sal allah ho alaihi wasallim), โWhat is the meaning of Ameen?โ
Muhammad (sal allah ho alaihi wasallim) said, โIt means, O Lord, undertake my grantโ
Trimidhi said, โIt means, [O Allah] donโt break our hopesโ
When one says Ameen over some prayer or Dua, it is as if he himself were praying to Allah, this is why when we say Ameen after the Imam recites Surah Al Fatiha, it is as we have also recited Surah Al Fatiha in Salah.
Let us make a habit of reciting Ameen whenever possible as it is one of the names of Allah.
Any mistake, on my part, if found, may please be forgiven.
JAZAAK ALLAH!