diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index bad289761..ae0c94b38 100644
--- a/Eigen/src/Core/Product.h
+++ b/Eigen/src/Core/Product.h
@@ -16,40 +16,6 @@ template<typename Lhs, typename Rhs, int Option, typename StorageKind> class Pro
 
 namespace internal {
 
-// Determine the scalar of Product<Lhs, Rhs>. This is normally the same as Lhs::Scalar times
-// Rhs::Scalar, but product with permutation matrices inherit the scalar of the other factor.
-// TODO: this could be removed once ScalarBinaryOpTraits handles void.
-template<typename Lhs, typename Rhs, typename LhsShape = typename evaluator_traits<Lhs>::Shape, 
-         typename RhsShape = typename evaluator_traits<Rhs>::Shape >
-struct product_result_scalar
-{
-  typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename RhsShape>
-struct product_result_scalar<Lhs, Rhs, PermutationShape, RhsShape>
-{
-  typedef typename Rhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename LhsShape>
-  struct product_result_scalar<Lhs, Rhs, LhsShape, PermutationShape>
-{
-  typedef typename Lhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename RhsShape>
-struct product_result_scalar<Lhs, Rhs, TranspositionsShape, RhsShape>
-{
-  typedef typename Rhs::Scalar Scalar;
-};
-
-template<typename Lhs, typename Rhs, typename LhsShape>
-  struct product_result_scalar<Lhs, Rhs, LhsShape, TranspositionsShape>
-{
-  typedef typename Lhs::Scalar Scalar;
-};
-
 template<typename Lhs, typename Rhs, int Option>
 struct traits<Product<Lhs, Rhs, Option> >
 {
@@ -60,7 +26,7 @@ struct traits<Product<Lhs, Rhs, Option> >
   
   typedef MatrixXpr XprKind;
   
-  typedef typename product_result_scalar<LhsCleaned,RhsCleaned>::Scalar Scalar;
+  typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
   typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,
                                                 typename RhsTraits::StorageKind,
                                                 internal::product_type<Lhs,Rhs>::ret>::ret StorageKind;