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.
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2026-03-27 00:02:49.1774569769
Prove set of free generators
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Hint: Notice that because a generator forms a group, $x^{-1},y^{-1}\in <x,y>$.
Can you take it from there?