Possible Numbers Of A In (a,b) Matrices With A Given Rank

Let a, b be two distinct real numbers. If each entry of a matrix is either a or b, then we call it an (a, b) matrix. In this paper, we mainly study the possible numbers of a in an (a, b) matrix with a given rank. First, we study the possible numbers of a in a generic nonsingular (a, b) matrix. Then we consider the case of symmetric matrices. Finally we investigate the structure of rank 2 symmetric (a, b) matrices and determine the possible numbers of a in such matrices.