All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The scholars have different opinions about the reason why there is no Basmalah (Bismillaahi Ar-Rahmaani Ar-Raheem –In the Name of Allaah, The Most Gracious, The Most Merciful) in Surah Tawbah [Quran 9], the most important of these opinions are the two following ones:
1- Its story is similar to that of Surah Al-Anfaal [Quran 8] and the Companions thought that it was a part of it and the Prophet died while not clarifying to them whether or not it is part of it. It for this reason that they placed them (in the Mus’haf) without writing Basmalah between them, and this is confirmed from ‘Uthmaan ibn Affaan in a tradition reported by At-Tirmithi and Al-Haakim .
2- It was reported that ‘Ali was asked about the reason for this and he said: “Al-Basmalah means peace, and Chapter 9 was revealed with a sword [i.e. ordering the believers to fight the disbelievers] and it does not include any peace.”
Allaah Knows best.