Strong shift equivalence of 2 by 2 non-negative integral matrices

Abstract

It is known that if A and B are nontriangular 2 x 2 non-negative integral matrices similar over the integers and -tr A less than or equal to det A, then A and B are strongly shift equivalent. Suppose that A and B are 2 x 2 non-negative integral matrices similar over the integers. In this article it is shown that if -2 tr A less than or equal to det A < -tr A and if \ det A\ is not a prime, then A and B are strongly shift equivalent.