A hybrid optical architecture for digital matrix-matrix multiplication is discussed. The proposed system requires less hardware than outer-product optical matrix multipliers and offers a higher processing speed than systolic array matrix multipliers. The throughput and hardware requirements of the proposed architecture are discussed with reference to the availability of various electro-optic devices. The performance of the proposed system is compared to existing systolic array optical matrix multipliers and to outer-product-based optical matrix processors. The accuracy and error rate of the proposed architecture are evaluated.