I have a question about salah that I learned from authentic source that for every rakah we pray there is a need to recite surah fatiha first other wise prayer will be invalid but on YouTube i watched a practical demonstration of Salah of shia school of thought in third and in fourth rakat they say it is mustahab to recite surah fatiha but they recite some thing else.

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Yes you are right according to shia Fiqh we recites “ Tasbeehat e Arba’ (four Tasbeeh) in our third and fourth Rak’at but if any one does not know the Tasbeehat Arba, they can recite Surah Al Hamd in his/her 3rd or 4th raka’at.
Now do we do so because this Zikr is one of the highly recommended zikr amongst all zikr. As you said the recommendation about Surah Al Hamd there is hadith that “There is no salat without Surah al Fatiha” and this covers 1st and 2nd Raka’at. Still one has choice, it’s not like we can’t recite Surah Al Fatiha at all and we have to recite only 4 Tasbeeh in our 3rd or4th rak’at. We have many Hadith from 12 Holy Imams regarding how Prophet (saww) used to pray and how 12 Imams used to Pray. So there is no doubt about the authenticity of what we have in practice.