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There are two parts of this problem. State whether each statement is true or false. Please...

There are two parts of this problem. State whether each statement is true or false. Please give a clear explanation of each.

a. Let G be a group and g in G. Define f : G → G by f(a) = (g-1)(a)(g) or f(a) = g-1ag, for all a in G.Then f is a permutation on G.

b. Let G/H be the set of left cosets of the subgroup H in G. If the operation given by the formula aHbH = abH is well-defined,then H is a normal subgroup of G.

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