diff --git a/pytensor/tensor/rewriting/math.py b/pytensor/tensor/rewriting/math.py
index 06d023d780..ba971c78da 100644
--- a/pytensor/tensor/rewriting/math.py
+++ b/pytensor/tensor/rewriting/math.py
@@ -190,6 +190,43 @@ def local_0_dot_x(fgraph, node):
             return [constant_zero]
 
 
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Dot])
+def local_1_dot_x(fgraph, node):
+    if not isinstance(node.op, Dot):
+        return False
+
+    x = node.inputs[0]
+    y = node.inputs[1]
+    replace = False
+    try:
+        if get_underlying_scalar_constant_value(x, only_process_constants=True) == 1:
+            replace = True
+            var = y
+    except NotScalarConstantError:
+        pass
+
+    try:
+        if get_underlying_scalar_constant_value(y, only_process_constants=True) == 1:
+            replace = True
+            var = x
+    except NotScalarConstantError:
+        pass
+
+    if replace:
+        new_out = var
+        old_out = node.outputs[0]
+
+        if new_out.dtype != old_out.dtype:
+            new_out = cast(new_out, old_out.dtype)
+        if not old_out.type.is_super(new_out.type):
+            new_out = new_out.reshape(old_out.shape)
+            # new_out = alloc_like(new_out, old_out, fgraph)
+
+        return [new_out]
+
+
 @register_canonicalize
 @node_rewriter([DimShuffle])
 def local_lift_transpose_through_dot(fgraph, node):
diff --git a/tests/tensor/rewriting/test_math.py b/tests/tensor/rewriting/test_math.py
index 84322989bf..a9b9c7138c 100644
--- a/tests/tensor/rewriting/test_math.py
+++ b/tests/tensor/rewriting/test_math.py
@@ -4475,3 +4475,22 @@ def test_local_batched_matmul_to_core_matmul():
     x_test = rng.normal(size=(5, 3, 2))
     y_test = rng.normal(size=(5, 2, 2))
     np.testing.assert_allclose(fn(x_test, y_test), x_test @ y_test)
+
+
+@pytest.mark.parametrize(
+    "x",
+    (
+        pt.col("x"),
+        fmatrix("x"),
+        vector("x"),
+        pt.tensor("x", shape=(1, 3, 2), dtype="float64"),
+    ),
+)
+def test_mul_with_1(x):
+    f = x @ [[1.0]]
+    with pytensor.config.change_flags(optimizer_verbose=True):
+        fn = pytensor.function([x], f, mode=get_default_mode().excluding("BlasOpt"))
+
+    pytensor.dprint(fn)
+
+    assert 0