Two m×n matrices A,B over a commutative ring R are equivalent
in case there are invertible matrices P, Q over R with B=PAQ. While any m×n matrix over a principle ideal domain
can be diagonalized, the same is not true for Dedekind domains. The first author and T. J. Ford
introduced a coarser equivalence relation on matrices called homotopy and showed any m×n matrix
over a Dedekind domain is homotopic to a direct sum of 1×2 matrices. In this article give,
necessary and sufficient conditions on a Prüfer domain that any m×n matrix be homotopic to a
direct sum of 1×2 matrices.