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Suppose we have $f:X\to Y$, where $f$ is a bijection. How would we show that $(f^{-1})^{-1}=f$

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    Thank you I completely understood it now. I was just missing that much I proved it and happy with the end result as well. Thanks for the tips.2012-10-08

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Hint: If $(x,y)\in f$ then $(y,x)\in f^{-1}$ and vice versa.

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    @user43964: You can use what Yunone noted you above as well. I think that approach is faster.2012-10-08