Exercise 5: (a) Show that permutations (12)(34), (13)(24), (14)(23), and the identical permutation e form a group under standard multiplication. This is the 'four-group'. We have x² = e for every element x of this group. (b) Assume that x = e for all elements x of a group G. Prove that G is abelian.

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A: Solution is given below:

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