عن ابن عباس قال: كان النبي -صلى الله عليه وسلم- لا يعرف فصل السورة حتى تنزل عليه {بسم الله الرحمن الرحيم}.
[صحيح] - [رواه أبو داود]
المزيــد ...

Ibn ‘Abbās (may Allah be pleased with him) reported: The Prophet (may Allah’s peace and blessings be upon him) did not know where Surahs were to be separated until "In the name of Allah, the Most Compassionate, the Most Merciful" was revealed to him.
Sahih/Authentic. - [Abu Dawood]

Explanation

The Prophet (may Allah’s peace and blessings be upon him) did not know where Surahs should be separated until the basmalah (in the name of Allah, the Most Compassionate, the Most Merciful) was revealed to him. In other words, when the basmalah was sent down, he would know that a Surah came to an end and a new one was being revealed. The basmalah is a verse that was revealed like the other verses. But, we may not read it at the beginning of Surat at-Tawbah, by analogy with the other Surahs. Also, if we begin the recitation from any place within a Surah, we are recommended not to say basmalah, according to this Hadīth, for the verse of basmalah was sent down at the beginning of Surahs. Some scholars disagree with this view, however.

Translation:
View Translations
1: The Hadīth indicates that basmalah is part of the Qur’an, since he described it as being 'revealed' to the Prophet (may Allah’s peace and blessings be upon him).
2: It denotes that basmalah is a verse that separates between Surahs, not part of the Surahs themselves. That is why it does not count as a verse and is not included in the number of verses, with the exclusion of Surat al-Fātihah, to which basmalah is added as one of its verses in the Mus-haf (bound copy of the Qur'an). The correct view, however, is that basmalah is an independent verse that does not belong to Al-Fātihah or any other Surah. An exception is Surat an-Naml in which basmalah occurs as part of one of its verses.
3: The basmalah is part of the Qur’an, and it separates Surahs from one another, as well known, except for Surat at-Tawbah and Surat al-Fātihah, because Al-Fātihah is preceded by no Surah. So, it begins with the basmalah, yet not for the sake of separating it from any other Surah. Surat at-Tawbah does not begin with basmalah.
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