Hashing functions and Universal Hashing Family

Question

I need to determine whether the following Hash Functions Set is universal or not: Let U be the set of the keys - {000, 001, 002, 003, ... ,999} - all the numbers between 0 and 999 padded with 0 in the beginning where needed. Let n = 10 and 1 < a < 9 ,an integer between 1 and 9. We denote by ha(x) the rightmost digit of the number a*x. For example, h2(123) = 6, because, 2 * 123 = 246. We also denote H = {h1, h2, h3, ... ,h9} as our set of hash functions. Is H is universal? prove.

I know I need to calculate the probability for collision of 2 different keys and check if it's smaller or equal to 1/n (which is 1/10), so I tried to separate into cases - if a is odd or even, because when a is even the last digit of a*x will be 0/2/4/6/8, else it could be anything. But it didn't help me so much as I'm stuck on it. Would be very glad for some help here.