Matrix multiplication is a fundamental operation in various scientific and engineering domains, and its efficiency is often measured by the matrix multiplication exponent, ω. This paper presents a review of existing algorithms designed to minimize ω, discussing their respective limitations, particularly in handling sparse matrices. We propose a novel method called Non-Zero Intersection Matrix Multiplication (NZIM), which is optimized for sparse matrix operations. NZIM focuses exclusively on non-zero elements, significantly reducing unnecessary computations and memory overhead, making it both computationally efficient and straightforward to implement. A detailed complexity analysis shows that NZIM is especially advantageous for sparse matrices, where it scales with the number of non-zero elements rather than matrix dimensions. Experimental results demonstrate that NZIM outperforms traditional algorithms as matrix sparsity increases, making it particularly suited for applications with large, sparse datasets, such as social network analysis and natural language processing. In conclusion, NZIM provides a well-balanced solution, offering high computational efficiency, reduced memory usage, and ease of implementation, especially for large-scale, sparse matrix scenarios.