Proving N(H) is a Subgroup of G to Normalizers in Group Theory

[wegmanstuna]

For a subgroup H of G and a fixed element a ∈ G,
let H^a = {x∈ G / axa^-1 ∈ H}, it's normalizer N(H) = {a∈G / H^a=H}

Show that for any subgroup H of G, N(H) is a subgroup of G.



I know that for the first one I need to show that closure holds, an identity exists, and inverses exist. But I don't even know where to start with closure!
Help!

 

[morphism]

If a and b are in N(H), write down what H^(ab) is. Now maybe you can try showing that H^{ab} \subset H and H \subset H^{ab}.