Salam Aleykum I forgot to send salutations on Prophet Muhammad (Sallallahu Alayhi Wa Sallam) then gave selam to my right and then remembered and did 2 rakah of forgetfulness and concluded the prayer IS MY PRAYER VALID ?

In regards to sending Salah upon the Messenger during your prayer, there are three sayings among the people of Ilm: 1. It is a Sunnah: According to this saying, if you have forgotten it, there is nothing on you. 2. It is mandatory: According to this saying, if you have forgotten it, it is corrected by performing Sujud As-Sahu. 3. It is a pillar: According to this saying, if you have forgotten it, your Salah is invalid. The first and the second sayings seem to be the strongest sayings, and Allah knows best.