A quick matrix multiplication algorithm is presented and evaluated on a cluster of networked workstations consisting of Pentium hosts connected together by Ethernet segments. The obtained results confirm the feasibility of using networked workstations to provide fast and low cost solutions to many computationally intensive applications such as large linear algebraic systems. The paper also presents and verifies an accurate timing model to predict the performance of the proposed algorithm on arbitrary clusters of workstations. Through this model the viability of the proposed algorithm can be revealed without the extra effort that would be needed to carry out real testing.