Ibn Abbas (Radhiallahuanhu) 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 have fasting on 9 and 10 both)
Sahih Muslim, Book 006, Number 2528
Abu Qatada al-Ansari (Radhiallahuanhu) reported that the Messenger of Allah (may peace be upon him) was asked about fasting on the day of ‘Ashura (10th of Muharram), whereupon he said: It expiates the sins of the preceding year.
Sahih Muslim, Book 006, Number 2603
we Can fast on 9th & 10th or 10th & 11