What is the ruling on congregants saying "Ameen" after the recitation of Al-Fatiha during prayer in the following situations: behind the Imam in an audible prayer, behind the Imam in a silent prayer, and for a solitary worshiper whether in an audible or silent prayer?

It is sunnah (definition) for the one praying alone to say "Ameen" after finishing the recitation of Surah (definition) Al-Fatiha, whether the prayer is silent or audible. The same applies to the Imam and the congregant in a silent prayer, and to the follower in an audible prayer if he hears the recitation of his Imam. As for the Imam in an audible prayer, the majority of scholars are of the opinion that it is recommended for him to say "Ameen," while the Malikis differ on this matter.