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There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix. Solving this recurrence relation, we found that the characteristic and the permanent polynomials can be calculated in terms of the characteristic and the permanent polynomials of some specific induced subdigraphs of blocks in the digraph, respectively. Interestingly, these induceddoi:10.1515/spma-2017-0010 fatcat:5g24mp6d5zczjbgbxg7wxakuxi