Need help in proving a*0 = 0

So far we know:

Axiom

1) a+b = b+a

2) (a+b)+c = a+(b+c)

3) There is a real number, called 0, so that a+0 = 0+a = a

4) a+(-a) = (-a)+a = 0

5) a * b = b * a

6) (a*b)*c = a*(b*c)

7) There is a real number called 1, with the properties that 1 is not equal to 0 and 1*a = a*1 = a

8) If a is not equal to 0, there is an element 1/a with the property that a*1/a = 1/a *a = 1

9) a*(b+c) = a*b+a*c