The Prophet ﷺ performed the two prostrations after the salutation.
حدثنا أحمد بن منيع حدثنا هشيم عن هشام بن حسان عن محمد بن سيرين
أن النبي ﷺ سجدهما بعد السلام
No references are available.
Agreed upon. Bukhari narrated it in the Book of Forgetfulness, Chapter on Saying the Takbeer in the Two Prostrations of Forgetfulness, hadith 1229, and Muslim, hadith 573, both from the hadith of Muhammad bin Sirin through this chain. It also appears at 399.