When the Prophet (sallallaahu ŭalaihi-wasallam) arrived in Al-Madinah, he found the Jews fasting on the tenth day of Muharram. He said,
''I am more entitled to follow Musa (Peace be upon him) than you.'' Reported Al-Bukhari in the Book of Fasting)
In the Hadith of Ibn Abbas, may Allaah be please with him, whose authenticity is agreed upon by Al-Bukhari and Muslim it is stated that the Prophet (sallallaahu ŭalaihi-wasallam) fasted on the Day of Ashuraŭ and he ordered that the fast be performed on it, and when he was asked about the virtue of fasting on it, he Prophet (sallallaahu ŭalaihi-wasallam) said,
''I anticipate that Allaah will wipe out the sins of the year before it, and the year after it'' (Reported By Muslim in the Book of Fasting)
However, after that, he commanded that the Muslims should be different from the Jews by fasting the tenth and the day before it, which is the ninth or the day after it, which is the eleventh.
Based upon this, it is preferable to fast on the tenth and to add a day before it or a day after it. Adding the ninth day to it is better than the eleventh.
So, my Muslim brother, it is desirable that you should fast on the Day of 'Ashura' and likewise on the ninth.