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Prove that if $X=\{x,y \}$ is a set of free generators then set $X^{-1} = \{x^{-1}, y^{-1} \}$ is also a set of free generators.

Have you got any ideas?

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Hint: Notice that because a generator forms a group, $x^{-1},y^{-1}\in $.

Can you take it from there?

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    It will be enough? But how can I prove that it generate the same group? – 2017-01-23
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    @json Can you show that e.g. $x\in\langle x^{-1}\rangle$? – 2017-01-23
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    I am not sure how to do it] – 2017-01-23
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    Hint: what is $(x^{-1})^{-1}$? – 2017-01-23
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    it is x. So is it a symmetric case? – 2017-01-23