Final answer:
The son-in-law and cousin of the Prophet Muhammad who was murdered after he became caliph was Ali ibn Abi Talib. His murder in 661 CE marked a significant moment in Islamic history, contributing to the enduring split between Sunni and Shia Islam.
Step-by-step explanation:
The son-in-law and cousin of Muhammad who was murdered after he became caliph was Ali ibn Abi Talib. The sequence of rulers known as the Rightly Guided Caliphs, following the death of the Prophet Muhammad, were Abu Bakr, Umar, Uthman, and finally Ali who was also Muhammad's cousin and son-in-law through his marriage to Fatima, Muhammad's daughter. Ali's caliphate was riddled with conflict and he was ultimately murdered in 661, marking a significant point in the origins of the split between the Sunni and the Shia sects of Islam. The resentments and challenges during his reign contributed to the First Fitna, the initial civil war within the Muslim community. This internal strife had lasting implications for the unity and political landscape of the Islamic world.