Incidence matrix is a useful tool for presenting incomplete block designs; however, it is inadequate to use only an incidence matrix in examining whether a certain incomplete block design becomes a balanced incomplete block design or not. We can use a structural matrix as a useful tool to show whether a certain incomplete block design becomes a balanced incomplete block design or not. We propose an augmented incidence matrix and ${lambda}$ matrix as another tools for evaluating incomplete block designs. Through the augmented incidenc matrix and ${lambda}$ matrix, we can ascertain whether a certain incomplete block design becomes a balance incomplete block design or not.