What is the order of a reaction if the rate constant has the units L-mol^-1s^-1?

Given the unit of the rate of the reaction is,

L-mol^-1s^-1

For second order,

$\text{ rate }=\mathrm{k}[\mathrm{A}{]}^2$

$\begin{array}{l}{\mathrm{molL}}^{-1}{\mathrm{s}}^{-1}=\mathrm{k}{\left({\mathrm{molL}}^{-1}\right)}^2\\ \mathrm{k}={\mathrm{Lmol}}^{-1}{\mathrm{s}}^{-1}\end{array}$