diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index 3c09a1d5..7e7294f8 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -10,7 +10,7 @@
 from hypothesis import assume, reject
 from hypothesis.strategies import (SearchStrategy, booleans, composite, floats,
                                    integers, complex_numbers, just, lists, none, one_of,
-                                   sampled_from, shared, builds, nothing)
+                                   sampled_from, shared, builds, nothing, permutations)
 
 from . import _array_module as xp, api_version
 from . import array_helpers as ah
@@ -148,6 +148,13 @@ def mutually_promotable_dtypes(
     return one_of(strats).map(tuple)
 
 
+@composite
+def pair_of_mutually_promotable_dtypes(draw, max_size=2, *, dtypes=dh.all_dtypes):
+    sample = draw(mutually_promotable_dtypes( max_size, dtypes=dtypes))
+    permuted = draw(permutations(sample))
+    return sample, tuple(permuted)
+
+
 class OnewayPromotableDtypes(NamedTuple):
     input_dtype: DataType
     result_dtype: DataType
diff --git a/array_api_tests/test_data_type_functions.py b/array_api_tests/test_data_type_functions.py
index f9642f31..e844c432 100644
--- a/array_api_tests/test_data_type_functions.py
+++ b/array_api_tests/test_data_type_functions.py
@@ -208,7 +208,53 @@ def test_isdtype(dtype, kind):
     assert out == expected, f"{out=}, but should be {expected} [isdtype()]"
 
 
-@given(hh.mutually_promotable_dtypes(None))
-def test_result_type(dtypes):
-    out = xp.result_type(*dtypes)
-    ph.assert_dtype("result_type", in_dtype=dtypes, out_dtype=out, repr_name="out")
+@pytest.mark.min_version("2024.12")
+class TestResultType:
+    @given(dtypes=hh.mutually_promotable_dtypes(None))
+    def test_result_type(self, dtypes):
+        out = xp.result_type(*dtypes)
+        ph.assert_dtype("result_type", in_dtype=dtypes, out_dtype=out, repr_name="out")
+
+    @given(pair=hh.pair_of_mutually_promotable_dtypes(None))
+    def test_shuffled(self, pair):
+        """Test that result_type is insensitive to the order of arguments."""
+        s1, s2 = pair
+        out1 = xp.result_type(*s1)
+        out2 = xp.result_type(*s2)
+        assert out1 == out2
+
+    @given(pair=hh.pair_of_mutually_promotable_dtypes(2), data=st.data())
+    def test_arrays_and_dtypes(self, pair, data):
+        s1, s2 = pair
+        a2 = tuple(xp.empty(1, dtype=dt) for dt in s2)
+        a_and_dt = data.draw(st.permutations(s1 + a2))
+        out = xp.result_type(*a_and_dt)
+        ph.assert_dtype("result_type", in_dtype=s1+s2, out_dtype=out, repr_name="out")
+
+    @given(dtypes=hh.mutually_promotable_dtypes(2), data=st.data())
+    def test_with_scalars(self, dtypes, data):
+        out = xp.result_type(*dtypes)
+
+        if out == xp.bool:
+            scalars = [True]
+        elif out in dh.all_int_dtypes:
+            scalars = [1]
+        elif out in dh.real_dtypes:
+            scalars = [1, 1.0]
+        elif out in dh.numeric_dtypes:
+            scalars = [1, 1.0, 1j]        # numeric_types - real_types == complex_types
+        else:
+            raise ValueError(f"unknown dtype {out = }.")
+
+        scalar = data.draw(st.sampled_from(scalars))
+        inputs = data.draw(st.permutations(dtypes + (scalar,)))
+
+        out_scalar = xp.result_type(*inputs)
+        assert out_scalar == out
+
+        # retry with arrays
+        arrays = tuple(xp.empty(1, dtype=dt) for dt in dtypes)
+        inputs = data.draw(st.permutations(arrays + (scalar,)))
+        out_scalar = xp.result_type(*inputs)
+        assert out_scalar == out
+