What is the wisdom behind saying "Ameen" after Al-Fatiha in prayer, and is it permissible to say it aloud or silently?

Saying "Ameen" after Al-Fatihah is a Sunnah. Scholars have differed on whether to say it aloud. One opinion holds that it should be said silently in all prayers because it is a supplication. Another opinion, which is the more preponderant one, is that it should be said aloud in audible prayers and silently in silent prayers. They based this on the fact that the Prophet, peace and blessings be upon him, raised his voice with it.

The meaning of "Ameen" is: "O Allah, answer (our prayer)."

Its virtues include: the answering of supplications, Allah's love for the one who says it, and the forgiveness of sins for anyone whose "Ameen" coincides with that of the angels. The Jews envied Muslims for "Ameen." It is recommended to say it frequently and to conclude supplications with it, as it is among the reasons for supplications to be answered.