Is “Duke Xiang of Qi had an affair with his sister Wen Jiang, wife of Duke Huan of Lu, and ordered Prince Peng Sheng to kill Duke Huan of Lu, then killed Peng Sheng to appease Lu.” true?

Both the Zuo Commentary, Duke Huan's 18th year, and the Records of the Grand Historian, Hereditary House of Qi, record that Duke Xiang of Qi had an affair with Wen Jiang, and had Peng Sheng ride in Duke Huan's carriage, causing Duke Huan to die in the carriage. When the people of Lu demanded an explanation, Duke Xiang 'then killed Peng Sheng to appease Lu,' vividly depicting the chaos of the Spring and Autumn period.