diff --git a/gtsam/geometry/tests/testPose2.cpp b/gtsam/geometry/tests/testPose2.cpp
index ca550cdc7..88976697a 100644
--- a/gtsam/geometry/tests/testPose2.cpp
+++ b/gtsam/geometry/tests/testPose2.cpp
@@ -172,6 +172,35 @@ TEST(Pose2, expmap_c_full)
   EXPECT(assert_equal(xi, Pose2::Logmap(expected),1e-6));
 }
 
+/* ************************************************************************* */
+// assert that T*exp(xi)*T^-1 is equal to exp(Ad_T(xi))
+TEST(Pose2, Adjoint_full) {
+  Pose2 T(1, 2, 3);
+  Pose2 expected = T * Pose2::Expmap(screwPose2::xi) * T.inverse();
+  Vector xiprime = T.Adjoint(screwPose2::xi);
+  EXPECT(assert_equal(expected, Pose2::Expmap(xiprime), 1e-6));
+
+  Vector3 xi2(4, 5, 6);
+  Pose2 expected2 = T * Pose2::Expmap(xi2) * T.inverse();
+  Vector xiprime2 = T.Adjoint(xi2);
+  EXPECT(assert_equal(expected2, Pose2::Expmap(xiprime2), 1e-6));
+}
+
+/* ************************************************************************* */
+// assert that T*wedge(xi)*T^-1 is equal to wedge(Ad_T(xi))
+TEST(Pose2, Adjoint_hat) {
+  Pose2 T(1, 2, 3);
+  auto hat = [](const Vector& xi) { return ::wedge<Pose2>(xi); };
+  Matrix3 expected = T.matrix() * hat(screwPose2::xi) * T.matrix().inverse();
+  Matrix3 xiprime = hat(T.Adjoint(screwPose2::xi));
+  EXPECT(assert_equal(expected, xiprime, 1e-6));
+
+  Vector3 xi2(4, 5, 6);
+  Matrix3 expected2 = T.matrix() * hat(xi2) * T.matrix().inverse();
+  Matrix3 xiprime2 = hat(T.Adjoint(xi2));
+  EXPECT(assert_equal(expected2, xiprime2, 1e-6));
+}
+
 /* ************************************************************************* */
 TEST(Pose2, logmap) {
   Pose2 pose0(M_PI/2.0, Point2(1, 2));
diff --git a/gtsam/geometry/tests/testPose3.cpp b/gtsam/geometry/tests/testPose3.cpp
index 98d3e11ee..d516ddc8b 100644
--- a/gtsam/geometry/tests/testPose3.cpp
+++ b/gtsam/geometry/tests/testPose3.cpp
@@ -143,6 +143,24 @@ TEST(Pose3, Adjoint_full)
   EXPECT(assert_equal(expected3, Pose3::Expmap(xiprime3), 1e-6));
 }
 
+/* ************************************************************************* */
+// assert that T*wedge(xi)*T^-1 is equal to wedge(Ad_T(xi))
+TEST(Pose3, Adjoint_hat)
+{
+  auto hat = [](const Vector& xi) { return ::wedge<Pose3>(xi); };
+  Matrix4 expected = T.matrix() * hat(screwPose3::xi) * T.matrix().inverse();
+  Matrix4 xiprime = hat(T.Adjoint(screwPose3::xi));
+  EXPECT(assert_equal(expected, xiprime, 1e-6));
+
+  Matrix4 expected2 = T2.matrix() * hat(screwPose3::xi) * T2.matrix().inverse();
+  Matrix4 xiprime2 = hat(T2.Adjoint(screwPose3::xi));
+  EXPECT(assert_equal(expected2, xiprime2, 1e-6));
+
+  Matrix4 expected3 = T3.matrix() * hat(screwPose3::xi) * T3.matrix().inverse();
+  Matrix4 xiprime3 = hat(T3.Adjoint(screwPose3::xi));
+  EXPECT(assert_equal(expected3, xiprime3, 1e-6));
+}
+
 /* ************************************************************************* */
 /** Agrawal06iros version of exponential map */
 Pose3 Agrawal06iros(const Vector& xi) {