diff --git a/lib/matplotlib/tests/test_transforms.py b/lib/matplotlib/tests/test_transforms.py
index 1501a918b9c8..064a7240c39d 100644
--- a/lib/matplotlib/tests/test_transforms.py
+++ b/lib/matplotlib/tests/test_transforms.py
@@ -10,7 +10,7 @@
import matplotlib.patches as mpatches
import matplotlib.transforms as mtransforms
from matplotlib.path import Path
-from matplotlib.testing.decorators import image_comparison
+from matplotlib.testing.decorators import image_comparison, check_figures_equal
def test_non_affine_caching():
@@ -730,3 +730,17 @@ def test_transformwrapper():
r"The input and output dims of the new child \(1, 1\) "
r"do not match those of current child \(2, 2\)")):
t.set(scale.LogTransform(10))
+
+
+@check_figures_equal(extensions=["png"])
+def test_scale_swapping(fig_test, fig_ref):
+ np.random.seed(19680801)
+ samples = np.random.normal(size=10)
+ x = np.linspace(-5, 5, 10)
+
+ for fig, log_state in zip([fig_test, fig_ref], [True, False]):
+ ax = fig.subplots()
+ ax.hist(samples, log=log_state, density=True)
+ ax.plot(x, np.exp(-(x**2) / 2) / np.sqrt(2 * np.pi))
+ fig.canvas.draw()
+ ax.set_yscale('linear')
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 59428b53e348..e263288a6aef 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -1732,6 +1732,7 @@ def set(self, child):
dimensions as the current child.
"""
if hasattr(self, "_child"): # Absent during init.
+ self.invalidate()
new_dims = (child.input_dims, child.output_dims)
old_dims = (self._child.input_dims, self._child.output_dims)
if new_dims != old_dims:
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