Group Action, Conjugates and Conjugation

Consider the group action of on itself via conjugation.
={ }, and
a) Find all the elements of that are fixed by the element r.
b) Let G be a group, and consider the action of G on itself via conjugation. Let g to G. Prove or disprove that the set of all elements of G that are fixed by g is a subgroup of G.
c) Find all the elements of that fix the element s.
d) Let G be a group, and consider the action of G on itself via conjugation. Let g G. Prove or disprove that the set of all elements of G that fix g is a subgroup of G.

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