Hi any help with these questions are greatly appreciated!

1) Let x, y, a, b be elements of a group G. (a) Show that x, x^(1), yxy^(1) all have the same order. (b) Using the fact that x and yxy^(1) have the same order, show that ab and ba have the same order. (c) Find three group elements a, b, c from the group of symmetries of the equilateral triangle such that the order of abc is not equal to the order of cba.

2)Let G be a group, and H be a subgroup of G. We define CG(H) = {x G : xh = hx, h H}. This is the set of all elements of G that commute with everything in H, called the centralizer of H in G.The set Z(G) = {x G : xg = gx, g G} is called the centre of G.(a) Show that CG(H) is a subgroup of G. b) Show that Z(G) is an abelian subgroup of G. (hint: Z(G) = CG(H) for some particular H)