First lets make the reflection material for the checkmate floor. This floor need to have some glossy surface with with specular point from the light. For making this select Phong for the Shader and set Specular Level to 90 and Glossiness to 75.
Next we have to set the Maps in our material. From Maps section click on Diffuse Color and select Checker from the list. Also click on Reflection and select Flat Mirror from the list