Right invariant extended Kalman filter (RIEKF) based simultaneous localization and mapping (SLAM) has shown to be able to produce more consistent SLAM estimates as compared with traditional EKF based SLAM methods. In this paper, RIEKF algorithm is used to solve active SLAM problem for 3D indoor environments with exploration task. A combined planner which combines an efficient global planner with an accurate local planner is proposed. Both the predicted SLAM results for candidate control actions and the actual estimated SLAM results after applying the selected control actions are computed using RIEKF algorithms. Simulation and real-world results under different scenarios have shown that the proposed RIEKF based active SLAM algorithm can explore unknown environments more efficiently with more accurate SLAM estimate. The code is made publicly available.