Matrix operations are fundamental to a wide range of scientific applications such as Graph Theory, Linear Equation System, Image Processing, Geometric Optics, and Probability Analysis. As the workload in these applications has increased, the sizes of matrices involved have also significantly increased. Parallel execution of matrix operations in existing cluster-based systems performs effectively for relatively small matrices but significantly suffers as matrices become larger due to limited resources. Cloud Computing offers scalable resources to handle this limitation; however, the benefits of having access to almost-infinite scalable resources in the Cloud also come with challenges of ensuring time and resource-efficient matrix operations. To the best of our knowledge, there is no specific Cloud service that optimizes the efficiency of matrix operations on Cloud infrastructure. To address this gap and offer convenient service of matrix operations, the paper proposes a novel scalable service framework called Scalable Matrix Operation as a Service. Our framework uses Dynamic Matrix Partition techniques, based on matrix operation and sizes, to achieve efficient work distribution, and scales based on demand to achieve time and resource-efficient operations. The framework also embraces the basic features of security, fault tolerance, and reliability. Experimental results show that the adopted dynamic partitioning technique ensures faster and better performance when compared to the existing static partitioning technique.