diff --git a/src/libsemigroups_pybind11/transf.py b/src/libsemigroups_pybind11/transf.py
index 912d5b52..80075ebd 100644
--- a/src/libsemigroups_pybind11/transf.py
+++ b/src/libsemigroups_pybind11/transf.py
@@ -123,6 +123,11 @@ def __ge__(self: Self, other) -> bool:
         return other < self or self == other
 
     def __mul__(self: Self, other: Self):
+        if self.degree() != other.degree():
+            raise ValueError(
+                "the arguments (transformations) must have equal degree, "
+                f"but found {self.degree()} and {other.degree()}"
+            )
         result = one(self)
         result.product_inplace(self, other)
         return result
diff --git a/src/transf.cpp b/src/transf.cpp
index 69920a0f..9e5126e0 100644
--- a/src/transf.cpp
+++ b/src/transf.cpp
@@ -733,7 +733,7 @@ fewer points requiring less space per point.
       m.def("transf_inverse",
             py::overload_cast<Perm_ const&>(&inverse<N, Scalar>));
     }  // bind_perm
-  }  // namespace
+  }    // namespace
 
   void init_transf(py::module& m) {
     // Transformations
diff --git a/tests/test_transf.py b/tests/test_transf.py
index 9d5bd65a..3ffbb6fa 100644
--- a/tests/test_transf.py
+++ b/tests/test_transf.py
@@ -300,3 +300,12 @@ def test_transf_return_policy():
         assert x.copy() is not x
         assert x.images() is not x.images()
         assert x.increase_degree_by(2) is x
+
+
+def test_transf_mult_diff_degrees():
+    for T in (Transf, PPerm, Perm):
+        x, y = T([0]), T([0, 1])
+        with pytest.raises(ValueError):
+            assert x * y == x
+        with pytest.raises(ValueError):
+            assert y * x == y