  There is a digraph corresponding to every square matrix over $\mathbb{C}$. We
generate a recurrence relation using the Laplace expansion to calculate the
characteristic, and permanent polynomials of a square matrix. Solving this
recurrence relation, we found that the characteristic, and permanent
polynomials can be calculated in terms of characteristic, and permanent
polynomials of some specific induced subdigraphs of blocks in the digraph,
respectively. Interestingly, these induced subdigraphs are vertex-disjoint and
they partition the digraph. Similar to the characteristic, and permanent
polynomials; the determinant, and permanent can also be calculated. Therefore,
this article provides a combinatorial meaning of these useful quantities of the
matrix theory. We conclude this article with a number of open problems which
may be attempted for further research in this direction.
