Eigen polynomial of 4*4 and 5*5 matrices in terms of determinants of their submatrices

The method to find the characteristic equation of a square matrix of any order is to solve the equation det.(A –λI ) = 0 i.e. | A – λI | = 0 which takes so much time when n = 4,5,…..& so on. This paper is an attempt to simplify the method to find the characteristic equation of a square matrix A of order 4 and 5 by taking the determinants of its all submatrices starting from 1x1 upto nxn.