Mapping/Left and right inverse/Inverse mapping/Exercise

Let ${}L$ and ${}M$ be sets and let

$F\colon L\longrightarrow M$

be a function. Let

$G\colon M\longrightarrow L$

be another function such that ${}F\circ G=\operatorname {Id} _{M}\,$ and ${}G\circ F=\operatorname {Id} _{L}\,$. Show that ${}G$ is the inverse of ${}F$.

Create a solution