This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model, comprising of 2 layers of explanatory variables-Matrix Multiplication, Performance and Semantic Explanations; and one layer of evidential variables containing 9 evidential variables-was developed. With the simulating data, 9 students' Performance and Semantic Explanation evidences were recorded. The results indicated that the hierarchical Bayesian assessment effectively traced and recorded students' learning trajectories; and assessed students' learning dynamically and diagnostically.