A real n by n matrix A is called an N(P)-matrix of exact order k, if the principal minors of A of order 1 through (n-k) are negative (positive) and (n-k+1) through n are positive (negative). In this paper the properties of exact order 1 and 2 matrices are investigated, using the linear complementarity problem LCP(q,A) for each q∈Rn. A complete characterization of the class of exact order 1 based on the number of solutions to the LCP(q,A) for each q∈Rn is presented. In the last section the authors consider the problem of computing a solution to the LCP(q,A) when A is a matrix of exact order 1 or 2.
