BUG: Multiindex.equals not commutative for ea dtype (pandas-dev#46047)

doc/source/whatsnew/v1.5.0.rst

@@ -350,7 +350,7 @@ Missing
 
 MultiIndex
 ^^^^^^^^^^
--
+- Bug in :class:`MultiIndex.equals` not commutative when only one side has extension array dtype (:issue:`46026`)
 -
 
 I/O

pandas/core/indexes/multi.py

@@ -3611,6 +3611,10 @@ def equals(self, other: object) -> bool:
                 # i.e. ExtensionArray
                 if not self_values.equals(other_values):
                     return False
+            elif not isinstance(other_values, np.ndarray):
+                # i.e. other is ExtensionArray
+                if not other_values.equals(self_values):
+                    return False
             else:
                 if not array_equivalent(self_values, other_values):
                     return False

pandas/tests/indexes/multi/test_equivalence.py

@@ -288,3 +288,11 @@ def test_multiindex_compare():
     expected = Series([False, False])
     result = Series(midx > midx)
     tm.assert_series_equal(result, expected)
+
+
+def test_equals_ea_int_regular_int():
+    # GH#46026
+    mi1 = MultiIndex.from_arrays([Index([1, 2], dtype="Int64"), [3, 4]])
+    mi2 = MultiIndex.from_arrays([[1, 2], [3, 4]])
+    assert not mi1.equals(mi2)
+    assert not mi2.equals(mi1)