diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
index 266529e7b..503a3d160 100644
--- a/Eigen/src/Geometry/AngleAxis.h
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -95,17 +95,17 @@ public:
   { return a * QuaternionType(b); }
 
   /** Concatenates two rotations */
-  inline typename ProductReturnType<Matrix3,Matrix3>::Type
+  inline Matrix3
   operator* (const Matrix3& other) const
   { return toRotationMatrix() * other; }
 
   /** Concatenates two rotations */
-  inline friend typename ProductReturnType<Matrix3,Matrix3>::Type
+  inline friend Matrix3
   operator* (const Matrix3& a, const AngleAxis& b)
   { return a * b.toRotationMatrix(); }
 
   /** Applies rotation to vector */
-  inline typename ProductReturnType<Matrix3,Vector3>::Type
+  inline Vector3
   operator* (const Vector3& other) const
   { return toRotationMatrix() * other; }
 
diff --git a/test/geometry.cpp b/test/geometry.cpp
index a3876c8d8..2bfdb04b4 100644
--- a/test/geometry.cpp
+++ b/test/geometry.cpp
@@ -65,8 +65,15 @@ template<typename Scalar> void geometry(void)
   VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
 
 
-  q1 = AngleAxis(ei_random<Scalar>(-M_PI, M_PI), v0.normalized());
-  q2 = AngleAxis(ei_random<Scalar>(-M_PI, M_PI), v1.normalized());
+  VERIFY_IS_APPROX(v0, AngleAxis(a, v0.normalized()) * v0);
+  VERIFY_IS_APPROX(-v0, AngleAxis(M_PI, v0.unitOrthogonal()) * v0);
+  VERIFY_IS_APPROX(cos(a)*v0.norm2(), v0.dot(AngleAxis(a, v0.unitOrthogonal()) * v0));
+  m = AngleAxis(a, v0.normalized()).toRotationMatrix().adjoint();
+  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxis(a, v0.normalized()));
+  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxis(a, v0.normalized()) * m);
+
+  q1 = AngleAxis(a, v0.normalized());
+  q2 = AngleAxis(a, v1.normalized());
 
   // rotation matrix conversion
   VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);