1. For a square: list all symmetries, draw Cayley table and find inverse of each symmetry....

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1. For a square: list all symmetries, draw Cayley table and find inverse of each symmetry. 2. For each of the following groups: determine order, draw Cayley table and find inverse of each element. a) C₁ = {e, x, x², 2³), where x¹ = e; b) Cs = {e.y.y², y³, y}, where y = e. Show and explain all steps. 1. For a square: list all symmetries, draw Cayley table and find inverse of each symmetry. 2. For each of the following groups: determine order, draw Cayley table and find inverse of each element. a) C₁ = {e, x, x², 2³), where x¹ = e; b) Cs = {e.y.y², y³, y}, where y = e. Show and explain all steps.