An operation $R$ is a right inverse of the operation $S$ in a set $A$ if for any elements $x,y,z∈A$ we have $x=yRz$ if, and only if, $y=zSx$
From this, for example multiplication is the right inverse of division (since $x=z·y$ if, and only if, $y=x÷z$) but in what set? $\mathbb R-\{0\}$ right?
Multiplication and division being inverse operations works on $K\setminus\{0\}$, where $K$ is any field. So, for example $$ \mathbb Q\setminus\{0\},\ \mathbb R\setminus\{0\},\ \mathbb C\setminus\{0\},\ \mathbb F_{p^n}\setminus\{0\},\ \dots $$