Abstract: A decorative and protective structural tile matrix for covering a base surface, such as a wall or countertop, is provided. A set of tiles comprise a subset of fixed tiles and a subset of removable tiles. The fixed tiles are permanently attached to the base surface by an adhesive. The removable tiles each provide a precast flexible grout sleeve of an elastomeric material, such as a plastic or rubber compound. The sleeve conforms to, and extends around, at least a portion of a peripheral edge of the removable tile. Each of the removable tiles takes a position between the fixed tiles such that the sleeve is compressed between the peripheral edges of the fixed tiles and the removable tile. As such, a compressive force is generated for holding each removable tile in place on the base surface. Alternatively, the sleeve is fixed to the base surface and has an outwardly extending frame defining pockets for insertion of a number of removable tiles.