Existing knowledge graph (KG) models for commonsense question answering present two challenges: (i) existing methods retrieve entities related to questions from the knowledge graph, which may extract noise and irrelevant nodes, and (ii) there is a lack of interaction representation between questions and graph entities. However, current methods mainly focus on retrieving relevant entities with some noisy and irrelevant nodes. In this paper, we propose a novel retrieval-augmented knowledge graph (RAKG) model, which solves the above issues using two key innovations. First, we leverage the density matrix to make the model reason along the corrected knowledge path and extract an enhanced subgraph of the knowledge graph. Second, we fuse representations of questions and graph entities through a bidirectional attention strategy, in which two representations fuse and update using a graph convolutional network (GCN). To evaluate the performance of our method, we conducted experiments on two widely used benchmark datasets: CommonsenseQA and OpenBookQA. The case study gives insight into the finding that the augmented subgraph provides reasoning along the corrected knowledge path for question answering.