Is this hadith authentic or not?
Prophet Muhammad (SAW) said, “There is no wudu for him who does not mention Allah’s name upon it.” (Sahih – Ibn Maajah, At-Tirmithee, Abu Dawood, and others)
جزاك الله كل خير
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A lot of the scholars have graded this hadeeth to be weak. among them is Imam Ahmed where he said that there is no hadeeth authentic on this topic.
All those who narrated the ablution of our Prophet salla Allahu alaihi wa sallam have never reported him saying bismillah.
Therefore, it is not mandatory to say it but it is highly recommended.