What is the authenticity of the saying that supplications are answered when the first drop of blood from the sacrificial animal falls, and that the one who offered the sacrifice will ride his sacrificial animal on the Day of Resurrection?

The riding of sacrificial animals on the Day of Resurrection is not established, nor do we know that supplication is answered when the blood of the sacrificial animal flows. It is authentically reported from the Prophet (peace and blessings be upon him) that he used to pronounce the name of Allah when slaughtering the sacrificial animal and supplicate for its acceptance, saying: "In the name of Allah, O Allah, accept this from Muhammad and the family of Muhammad and the Ummah of Muhammad."