# Definition Consider a [[Types of Maps|bijective]] [[map]] $f: X\rightarrow Y$ defined by $f: x \mapsto f(x)$. We can define an *inverse map*, which is also a bijection, by $f^{-1}:Y\rightarrow X$ such that $f^{-1}: f(x) \rightarrow x$. The maps $f$ and $f^{-1}$ satisfy the following identities $ \begin{align} f \circ f^{-1} &= \text{id}_{Y}, \\ f^{-1} \circ f &= \text{id}_{X} \end{align} $ where $\text{id}_{.}$ is the [[Identity Map]].