There are many complex issues with incomplete data to make decisions in the field of computer science. These issues can be resolved with the aid of mathematical instruments. When dealing with incomplete data, rough set theory is a useful technique. In the classical rough set theory the information granules are equivalence classes. However, in real life scenario tolerance relations play a major role. By employing rough sets with Maximal Compatibility Blocks (MCBs) rather than equivalence classes, we were able to handle the challenges in this research with ease. A novel approach to define matrices on MCBs and operations on them is proposed. Additionally, applied the rough matrix approach to locate a consistent block related to any set in the universal set.