Question

Let G be a group such that x² = 1 for all x € G (that is, every element squares to the identity element). Show that G is abelian. Let G ={1, a,b,c} be a group of order 4 such that 2 = 1 for all a E G. Construct the Cayley table of G. Which group already met in lectures has the same pattern of entries inits Cayley table? Can you construct other examples of groups G, with different orders, that satisfy the condition that x² = 1 for all x € G?

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