diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index b259f182a1197..1ae76984484af 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -185,7 +185,7 @@ Timezones
 
 Numeric
 ^^^^^^^
--
+- Bug in operations with array-likes with ``dtype="boolean"`` and :attr:`NA` incorrectly altering the array in-place (:issue:`45421`)
 -
 
 Conversion
diff --git a/pandas/core/arrays/boolean.py b/pandas/core/arrays/boolean.py
index 0ba98e4a377ae..5e72b2b3af631 100644
--- a/pandas/core/arrays/boolean.py
+++ b/pandas/core/arrays/boolean.py
@@ -494,7 +494,8 @@ def _arith_method(self, other, op):
         if mask is None:
             mask = self._mask
             if other is libmissing.NA:
-                mask |= True
+                # GH#45421 don't alter inplace
+                mask = mask | True
         else:
             mask = self._mask | mask
 
diff --git a/pandas/tests/arrays/masked/test_arithmetic.py b/pandas/tests/arrays/masked/test_arithmetic.py
index ab6e5110422ca..61775a2b94107 100644
--- a/pandas/tests/arrays/masked/test_arithmetic.py
+++ b/pandas/tests/arrays/masked/test_arithmetic.py
@@ -47,7 +47,7 @@ def test_array_scalar_like_equivalence(data, all_arithmetic_operators):
         tm.assert_extension_array_equal(result, expected)
 
 
-def test_array_NA(data, all_arithmetic_operators, request):
+def test_array_NA(data, all_arithmetic_operators):
     data, _ = data
     op = tm.get_op_from_name(all_arithmetic_operators)
     check_skip(data, all_arithmetic_operators)
@@ -55,8 +55,14 @@ def test_array_NA(data, all_arithmetic_operators, request):
     scalar = pd.NA
     scalar_array = pd.array([pd.NA] * len(data), dtype=data.dtype)
 
+    mask = data._mask.copy()
     result = op(data, scalar)
+    # GH#45421 check op doesn't alter data._mask inplace
+    tm.assert_numpy_array_equal(mask, data._mask)
+
     expected = op(data, scalar_array)
+    tm.assert_numpy_array_equal(mask, data._mask)
+
     tm.assert_extension_array_equal(result, expected)