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Exercise 2.8 (Solutions)

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eft( {{a}^{-1}}*a \right)*x={{a}^{-1}}*b\,\,\,\, \text{by associative law}\\ \Rightarrow \,\,\,\,& e*x={{a}^{-1}}*b \,\,\,\,\text{by inverse law.}\\ \Rightarrow \,\,\,\,& x={{a}^{-1}}*b\,\,\,\, \text{by identity law.}\end{align} And for \begin{ali... \,\,& \left( x*a \right)*{{a}^{-1}}=b*{{a}^{-1}} \text{ for } a \in G, {{a}^{-1}}\in G \\ \Rightarrow \,