So we muslims fast on 9 and 10 both

✦ Narrated Ibn Abbas Radi allahu anhu : The Prophet Sal-Allahu Alaihi Wasallam came to Medina and saw the Jews fasting on the day of Ashura. He asked them about that. They replied, "This is a good day, the day on which Allah rescued Bani Israel from their enemy. So, Moses fasted this day." The Prophet Sal-Allahu Alaihi Wasallam said, "We have more claim over Moses than you." So, the Prophet fasted on that day and ordered (the Muslims) to fast (on that day).

Sahih Bukhari Vol3, 2004

✦ Ibn Abbas Radi Allahu Anhu reported that when the Messenger of Allah (may peace be upon him) fasted on the day of Ashura and commanded that it should he observed as a fast, they (his Companions) said to him: Messenger of Allah, it is a day which the Jews and Christians hold in high esteem. Thereupon the Messenger of Allah (may peace be upon him) said: When the next year comes, God willing, we would observe fast on the 9th But the Messenger of Allah peace be upon him passed away before the advent of the next year.

(So we muslims fast on 9 and 10 both)

Sahih Muslim, Book 6, 2528