Secure distributed matrix multiplication (SDMM) is a core technique to solve data privacy leakage and node straggler problems in large-scale distributed computation. Most existing polynomial coding frameworks of secure distributed matrix computation (SDMC) are based on the semi-honest security model and lack lightweight mechanisms to identify Byzantine malicious nodes that tamper with calculation results. To solve this problem, this paper proposes a Byzantine fault-tolerant verification extension scheme for active result tampering scenarios. While retaining the privacy protection capability of the traditional polynomial masking scheme, the proposed scheme introduces a redundant replication strategy and combines it with element-wise robust median aggregation to effectively mitigate data poisoning attacks. Furthermore, it deploys a lightweight statistical verification layer, which detects and isolates malicious nodes through Frobenius norm deviation scores. Theoretical analysis demonstrates that the scheme can realize the accurate reconstruction of matrix products when the number of malicious nodes meets the honest majority threshold condition. Experimental results show that the proposed scheme has excellent scalability when the matrix dimension increases from 32 to 512, and its runtime overhead ratio drops significantly from 4.86 to 1.06. Independent of complex cryptographic proof mechanisms, the proposed scheme provides a highly scalable, verifiable and Byzantine fault-tolerant solution for matrix multiplication operations in decentralized cloud environments.