linear algebra - Eigenvalues of product of p.d. Matrix with upper-triangular Matrix

Let $A$ be a positive definite matrix (positive eigenvalues). Let $B$ be an upper triangular matrix, with ones in its main diagonal (i.e. all its eigenvalues are 1). Is there anything I can say about the eigenvalues of $AB$ ? I would like to find a way to prove that $AB$ has positive eigenvalues, if that's true.
Thanks.