What is the opinion of the four schools of thought and their evidence regarding saying "Amin" in prayer, and what is the effect of not saying "Amin" aloud after Al-Fatiha in it?

Summary of the question: Saying "Ameen" after Al-Fatiha is a Sunnah (definition) for the Imam, the congregant, and the individual according to the majority of scholars. The Malikis, however, state that it is not recommended for the Imam to say "Ameen", but it is recommended for the congregant and the individual. If one omits saying "Ameen", their prayer is valid and not nullified by its omission, nor is a prostration of forgetfulness required for its omission. In fact, according to the Malikis, if one prostrates for its omission, their prayer becomes invalid.