I need help in another subgroup problem...

please help!

--->Assume that G is a subgroup with operation * and that a E G. Let..

C(a) = { x E G : a *x = x*a}.

prove that C(a) is a subgroup of G?

using the property..

Let G be a group with operation * and let H be a subset of G. Then H is a subgroup of G if and only if:

1) H is non empty.

2) If a E H and b E H then a*b E H

3) If a E H then a(inverse) E H.