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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There are some authentic Ahaadeeth encouraging Muslims to recite the Basmalah at the beginning of their actions. For instance, the Prophet, sallallaahu ‘alayhi wa sallam, said: “Any matter of importance which is not begun with the remembrance of Allaah remains defective.” [Ahmad, Ibn Maajah and others] The same Hadeeth was reported with a slightly different wording; “Any matter of importance which is not begun with the remembrance of Allaah and with Basmalah remains defective.”
Another version of the same Hadeeth reads, “Any matter of importance which is not begun with Alhamdu-lillaah (praise be to Allaah) remains defective.” [Ibn Hibbaan - Al-Albaani graded it Hasan (good)]
We do not know of a reported Hadeeth indicating that the Prophet recited Basmalah before every action. Nevertheless, Muslim jurists recommended reciting the Basmalah at the beginning of all acts be it an act of worship like Ghusl (ritual bath), Wudhoo’ (ablution), Tayammum (dry ablution), recitation of the Quran, or any other (worldly) permissible act such as eating, drinking, or having intercourse with one’s spouse and the like.
Also, it is reported that the Prophet, sallallaahu ‘alayhi wa sallam, used to begin his letters with the Basmalah following the example of Prophet Sulaymaan (Solomon) as reported in the Quran. Allaah, The Exalted, says (what means): {Indeed, it is from Solomon, and indeed, it reads: 'In the name of Allaah, the Entirely Merciful, the Especially Merciful.} [Quran 27:30]
For example, it was reported that the Prophet, sallallaahu ‘alayhi wa sallam, wrote to Heraclius, Ceasar of the Byzantine Empire: “In the Name of Allaah, The Most gracious, The Most Merciful. This is a letter from Muhammad, the slave and Messenger of Allaah ...”
Moreover, Jibreel (Gabriel) descended to the Prophet, sallallaahu ‘alayhi wa sallam, and revealed to him the Basmalah at the beginning of each Surah of the Quran and thus, the Prophet, sallallaahu ‘alayhi wa sallam, knew the beginning and end of each Surah.
In Al-Itqaan, Imaam As-Suyooti wrote, "Abu Daawood, Al-Haakim, Al-Bayhaqi and Al-Bazzaar reported on the authority of Sa‘eed ibn Jubayr that Ibn ‘Abbaas said, ‘The Prophet, sallallaahu ‘alayhi wa sallam, did not know where a chapter of the Quran ended until the Basmalah was revealed to him.’ Al-Bazzaar added, ‘When the Basmalah was revealed to him, he, sallallaahu ‘alayhi wa sallam, would know that the chapter ended and another chapter started.’ In addition, it was reported on the authority of Sa‘eed Ibn Jubayr through another chain of narrators that Ibn ‘Abbaas said, ‘Muslims did not know the end of the chapters of the Quran except when the Basmalah was revealed to the Prophet, sallallaahu ‘alayhi wa sallam; once it was revealed, they knew the end of the chapter of the Quran.’ [Al-Haakim: It is in accordance with the criteria of Al-Bukhari and Muslim] Moreover, Al-Haakim narrated through a different chain of narrators that Ibn ‘Abbaas said, ‘Whenever Jibreel descends to the Prophet, sallallaahu ‘alayhi wa sallam, revealing to him the Basmalah, he, sallallaahu ‘alayhi wa sallam, would know that a new chapter of the Quran was revealed.’ [Saheeh (sound)] Ibn Mas‘ood said, ‘We did not know of any separation between two chapters of the Quran except after the Basmalah was revealed.’ [Al-Bayhaqi and others]’' [End of quote]
Allaah Knows best.