1. Define an operation * on the set G = {(x, y) = RR | x...

 

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1. Define an operation * on the set G = {(x, y) = RR | x 0} by (a, b) * (c, d) = (ac, ad + bc). 2. Prove that (G, *) is an abelian group. Let a, b, c, x be elements of a group G. Solve the following systems of equations for x: (a) ax2 = cx cx-1 and x4 = b (b) xc cbxa-1 and xca = cax 1. Define an operation * on the set G = {(x, y) = RR | x 0} by (a, b) * (c, d) = (ac, ad + bc). 2. Prove that (G, *) is an abelian group. Let a, b, c, x be elements of a group G. Solve the following systems of equations for x: (a) ax2 = cx cx-1 and x4 = b (b) xc cbxa-1 and xca = cax