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Elements x and y of a group G are called conjugate if y = z-1xz for some z ∈ G.
(a) Show that ab and ba are conjugate for any a, b ∈ G.
(b) Define a relation R on G by (x, y) ∈ R if and only if x and y are conjugate inG. Show that R is an equivalence relation. The equivalence classes for this relation arecalled conjugacy classes.
(c) How many conjugacy classes does the symmetric group G = S3 have? Write outthe elements of each conjugacy class
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