  Broline, Crowe and Isaacs have computed the determinant of a matrix
associated to a Conway-Coxeter frieze pattern. We generalise their result to
the corresponding frieze pattern of cluster variables arising from the
Fomin-Zelevinsky cluster algebra of type A. We give a representation-theoretic
interpretation of this result in terms of certain configurations of
indecomposable objects in the root category of type A.
