In order to test the effectiveness of multi-dimensional N-back task for inducing deeper brain fatigue, we conducted a series of N*L-back experiments: 1*1-back, 1*2-back, 2*1-back and 2*2-back tasks. We analyzed and compared the behavioral results, EEG variations and mutual information among these four different tasks. There was no significant difference in average EEG power and power spectrum entropy (PSE) among the tasks. However, the behavioral result of N*2-back task showed significant difference compared to traditional one dimensional N-back task. Connectivity changes were observed with the addition of one more matching task in N-back. We suggest that multi-dimensional N-back task consume more brain resources and activate different brain areas. These results provide a basis for multi-dimensional N-back tasks that can be used to induce deeper mental fatigue or exert more workload.