This invention relates to a flooring system comprised of a plurality of washable, multi-component floor mats. The floor mats contain a textile component and a base component. The textile component and the base component are attached to one another by a variety of mechanisms, including magnetic attraction. The magnetic attraction is provided by incorporation of magnetic particles in both the textile and base components. The textile component is designed to be soiled, washed, and re-used, thereby providing ideal end-use applications in areas such as building entryways.