If alpha is even prove that alpha-1 is also even does a

Question

Question 1- If α is even, prove that α^-1 is also even. Does a corresponding result hold if α is odd?

Question 2- List the left and right cosets of the subgroups in each of the following.

(a) (8) in Z₂₄

(b) (3) in U(8)

(c) 3Z in Z

(d) A₄ in S₄

(e) A_n in S_n

(f)  D₄ in S₄

(g) T in C*

(h) H = {(1), (123),(132)} in S₄

Question 3- Using Fermat's little theorem show that 63 is not prime.