diff --git a/mpmath/matrices/matrices.py b/mpmath/matrices/matrices.py
index b5ef40f4..44b75b8e 100644
--- a/mpmath/matrices/matrices.py
+++ b/mpmath/matrices/matrices.py
@@ -205,9 +205,15 @@ class _matrix(object):
          ['2.0', '3.0']])
 
     Of course you can perform matrix multiplication, if the dimensions are
-    compatible::
+    compatible, using ``@`` (for Python >= 3.5) or ``*``. For clarity, ``@`` is
+    recommended (`PEP 465 <https://www.python.org/dev/peps/pep-0465/>`), because
+    the meaning of ``*`` is different in many other Python libraries such as NumPy.
 
-        >>> A * B
+        >>> A @ B # doctest:+SKIP
+        matrix(
+        [['8.0', '22.0'],
+         ['14.0', '48.0']])
+        >>> A * B # same as A @ B
         matrix(
         [['8.0', '22.0'],
          ['14.0', '48.0']])
@@ -215,6 +221,10 @@ class _matrix(object):
         matrix(
         [['2.0']])
 
+    ..
+        COMMENT: TODO: the above "doctest:+SKIP" may be removed as soon as we
+        have dropped support for Python 3.4 and below.
+
     You can raise powers of square matrices::
 
         >>> A**2
@@ -233,6 +243,8 @@ class _matrix(object):
         [['1.0', '1.0842021724855e-19'],
          ['-2.16840434497101e-19', '1.0']])
 
+
+
     Matrix transposition is straightforward::
 
         >>> A = ones(2, 3)
@@ -592,6 +604,9 @@ class _matrix(object):
                     new[i, j] = other * self[i, j]
             return new
 
+    def __matmul__(self, other):
+        return self.__mul__(other)
+
     def __rmul__(self, other):
         # assume other is scalar and thus commutative
         if isinstance(other, self.ctx.matrix):
diff --git a/mpmath/tests/test_matrices.py b/mpmath/tests/test_matrices.py
index 25fdd697..04452031 100644
--- a/mpmath/tests/test_matrices.py
+++ b/mpmath/tests/test_matrices.py
@@ -1,4 +1,5 @@
 import pytest
+import sys
 from mpmath import *
 
 def test_matrix_basic():
@@ -48,6 +49,19 @@ def test_matrix_basic():
     assert A9 != A10
     assert nstr(A9)
 
+def test_matmul():
+    """
+    Test the PEP465 "@" matrix multiplication syntax.
+    To avoid syntax errors when importing this file in Python 3.4 and below, we have to use exec() - sorry for that.
+    """
+    # TODO remove exec() wrapper as soon as we drop support for Python <= 3.4
+    if sys.hexversion < 0x30500f0:
+        # we are on Python < 3.5
+        pytest.skip("'@' (__matmul__) is only supported in Python 3.5 or newer")
+    A4 = matrix([[1, 2, 3], [4, 5, 6]])
+    A5 = matrix([[6, -1], [3, 2], [0, -3]])
+    exec("assert A4 @ A5 == A4 * A5")
+
 def test_matrix_slices():
     A = matrix([    [1, 2, 3],
                         [4, 5 ,6],