In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- The consensus among Muslims has been that the Prophet was born in the ‘Year of the Elephant’, and it was precisely in the month of Rabi` al Awwal, and it was on a Monday.
2- There is consensus that Prophet Muhammad died on Monday, in the month of Rabi“` Al-Awwal, in the 11th year of Hijrah.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
When was Prophet Muhammad born?
The consensus among Muslims has been that the Prophet (peace be upon him) was born in the ‘Year of the Elephant‘, and it was precisely in the month of Rabi` al Awwal, and it was on a Monday. However, as for the precise date, while most scholars put it on the 12th, some others place it on the 9th.
The Prophet (peace be upon him) was asked why he fasted on Mondays; he replied, ‘it is the day I was born, and it is the day I was entrusted with the mission of Prophethood. (Muslim)
Some prominent authors of Seerah, including Muhammad Khudri and Safiuddin Mubarakakuri, have endorsed the view of Mahmud Pasha, the famous Egyptian astronomer, that he was born on Monday, the 9th of Rabi` al-Awwal, which corresponded to the 20th of April, in the year of 571 CE, which, also corresponds to the year of the Elephant. He was born in the house of his uncle Abu Talib, in the valley of Banu Hashim (Cf. Muhammad Khudri Bek, Nur al-Yaqin, p. 9.)
When did Prophet Muhammad die?
Almighty Allah knows best.