What is the ruling on someone who doubted whether he had performed the bowing (rukuʿ) while in prostration (sujud) during the second rakʿah, then stood up to perform it, but then remembered that he had already performed it? Should he complete the extra bowing or return to prostration?

If you are certain or highly assume that you have performed the bowing (rukūʿ) whose omission was doubted, the correct action is to return directly to prostration (sujūd). It is legislated for you to perform the prostration of forgetfulness (sujūd al-sahw) after the salutation (salām). The prayer is not invalidated by completing this extra bowing out of ignorance or forgetfulness. However, if one performs it intentionally, it invalidates the prayer. The prostration of forgetfulness is sufficient whether performed before or after the salutation.