Let G = S3, the symmetric group of degree 3 and let H = {i,f} where f(x1) = x2, f(x2) = x1, f(x3) = x3

a) find all the left cosets of H in G

b) find all the right cosets of H in G

c) Is every left coset of H a right coset of H?

Please show explicit steps I'm very confused on how to prove these coset problems. Thanks so much!