Is “Fuchai gave a sword and forced Wu Zixu to commit suicide, and Wu Zixu asked to have his eyes gouged out and hung on the eastern gate of Wu to watch the Yue army destroy Wu.” true?

According to Records of the Grand Historian, Biography of Wu Zixu, Wu Yuan said before his death: 'Gouge out my eyes and hang them on the eastern gate of Wu, so that I may see the Yue invaders come to destroy Wu.' Fuchai was furious, took his body, put it in a leather bag, and floated it in the river. The cruelty recorded in official history even exceeds that in the novel.