We describe an Ulrich module on the coordinate ring of the projective hypersurface X defined by the determinant of an n × n linear matrix ϕ , and show that the module defines a vector bundle on X if and only if the ideal generated by the n − 1 order minors of ϕ is zero-dimensional; this property does not force X to be smooth, while the existing literature focuses on the smooth case. If X is any smooth hypersurface, we characterize when its derivation module is Ulrich. We raise the same question in higher codimension and show the Segre threefold has this property.