* Blind obedience to Voldemort: Bellatrix was a fervent follower of Voldemort, believing in his vision of a pure-blood wizarding world. She saw Sirius as a traitor to the cause, having been falsely accused of murdering Peter Pettigrew and joining the Order of the Phoenix.
* Personal animosity: Bellatrix had always been a cruel and sadistic person. She held a deep-seated hatred for Sirius, stemming from their family rivalry and his association with the Light side. She relished the opportunity to inflict pain and suffering on him.
* Desire for approval: Bellatrix craved Voldemort's approval and saw this as an opportunity to prove her loyalty. By killing a member of the Order, she was demonstrating her commitment to the Dark Lord's cause.
* Delusions of grandeur: Bellatrix believed she was superior to her cousins, seeing herself as a true follower of Voldemort and Sirius as a weakling. She viewed the murder as a way to assert her dominance and establish herself as a powerful figure in the Dark Lord's ranks.
It's important to remember that Bellatrix's actions were not driven by logic or reason, but by a twisted sense of loyalty, hatred, and a desire to prove her worth to Voldemort. Her actions were a product of her deeply disturbed personality and her unwavering commitment to the Dark Lord's cause.