Let G be a group and H be the subgroup of G, not necessarily normal. Show that 91 =1 92 mod H =- 91 =r g, mod H Conclude that the function f : G/H - H\\G given by f(gH) = Hg -1 is well defined. Note that G/ H is the quotient group and H\\G is the right cosets of H. i.e. does not depend on the choice of the representative for gH. Then, show that f defines a bijection from G/H to H\\G by finding an inverse function. (Hint: the function F : G/H - H\\G given by F(gH) = Hg is well-defined if and only if H is normal)