diff --git a/pymatsolver/solvers.py b/pymatsolver/solvers.py
index e4cba32..3c403b4 100644
--- a/pymatsolver/solvers.py
+++ b/pymatsolver/solvers.py
@@ -40,6 +40,9 @@ class Base(ABC):
         Extra keyword arguments. If there are any left here a warning will be raised.
     """
 
+    __numpy_ufunc__ = True
+    __array_ufunc__ = None
+
     def __init__(
             self, A, is_symmetric=None, is_positive_definite=False, is_hermitian=None, check_accuracy=False, check_rtol=1e-6, check_atol=0, accuracy_tol=None, **kwargs
     ):
diff --git a/tests/test_Basic.py b/tests/test_Basic.py
index faf287a..125b1a8 100644
--- a/tests/test_Basic.py
+++ b/tests/test_Basic.py
@@ -55,6 +55,9 @@ def test_basic_solve():
     npt.assert_equal(Ainv @ rhs2d, rhs2d)
     npt.assert_equal(Ainv @ rhs3d, rhs3d)
 
+    npt.assert_equal(rhs @ Ainv, rhs)
+    npt.assert_equal(rhs.T * Ainv, rhs)
+
 
 # use Diagonal solver as a concrete instance of the Base to test for some errors
 
@@ -86,4 +89,16 @@ def test_errors_and_warnings():
         IdentitySolver(np.full((4, 4), 1), check_rtol=0.0)
 
     with pytest.raises(ValueError, match="check_atol must.*"):
-        IdentitySolver(np.full((4, 4), 1), check_atol=-1.0)
\ No newline at end of file
+        IdentitySolver(np.full((4, 4), 1), check_atol=-1.0)
+
+    with pytest.raises(ValueError, match="Expected a vector of length.*"):
+        Ainv = IdentitySolver(np.eye(4, 4))
+        Ainv @ np.ones(3)
+
+    with pytest.raises(ValueError, match="Second to last dimension should be.*"):
+        Ainv = IdentitySolver(np.eye(4, 4))
+        Ainv @ np.ones((3, 2))
+
+    with pytest.warns(FutureWarning, match="In Future pymatsolver v0.4.0, passing a vector.*"):
+        Ainv = IdentitySolver(np.eye(4, 4))
+        Ainv @ np.ones((4, 1))
\ No newline at end of file