Did Yazid ibn Muawiyah order the killing of Hussein ibn Ali, and did Abd al-Malik ibn Marwan order the killing of the sons of Al-Zubayr?

It is established that the killing of Husayn (may Allah be pleased with him) occurred during the caliphate of Yazid ibn Mu'awiyah, and the killing of Abdullah ibn Al-Zubayr (may Allah be pleased with him) occurred in the battle led by Al-Hajjaj in Mecca, with the permission and order of Abd al-Malik ibn Marwan. Abd al-Malik did not fully assume sovereignty until after the killing of Ibn Al-Zubayr.