Show that the group {e, a, b, c} with multiplication table (b) below, is in one to

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Show that the group {e, a, b, c} with multiplication table (b) below, is in one to one correspondence with the geometrical symmetry operations on figure (a) below

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This is called the 4-group or dihedral group \(\mathrm{D}_{2}\). Show that \(\mathrm{D}_{2}\) has three subgroups, \(\{e, a\},\{e, b\}\), and \(\{e, c\}\), each isomorphic to the cyclic group \(\mathrm{C}_{2}\).

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