diff --git a/mlx/backend/cpu/matmul.cpp b/mlx/backend/cpu/matmul.cpp
index 8ae99ab2d..b944aacc0 100644
--- a/mlx/backend/cpu/matmul.cpp
+++ b/mlx/backend/cpu/matmul.cpp
@@ -132,6 +132,10 @@ void AddMM::eval_cpu(const std::vector<array>& inputs, array& out) {
     throw std::runtime_error(
         "[AddMM::eval_cpu] Currently only supports float32.");
   }
+  if (out.size() == 0) {
+    out.set_data(allocator::malloc(out.nbytes()));
+    return;
+  }
 
   // Fill output with C
   auto& c = inputs[2];
@@ -139,7 +143,9 @@ void AddMM::eval_cpu(const std::vector<array>& inputs, array& out) {
       ? CopyType::Scalar
       : (c.flags().row_contiguous ? CopyType::Vector : CopyType::General);
   copy(c, out, ctype, stream());
-
+  if (inputs[0].shape(-1) == 0) {
+    return;
+  }
   matmul_general(inputs[0], inputs[1], out, stream(), alpha_, beta_);
 }
 
diff --git a/mlx/backend/metal/matmul.cpp b/mlx/backend/metal/matmul.cpp
index 71221f8d9..e0ff44200 100644
--- a/mlx/backend/metal/matmul.cpp
+++ b/mlx/backend/metal/matmul.cpp
@@ -716,6 +716,23 @@ void AddMM::eval_gpu(const std::vector<array>& inputs, array& out) {
     throw std::runtime_error(
         "[matmul] Does not yet support non-floating point types.");
   }
+
+  // Return 0s if either input is empty
+  if (out.size() == 0) {
+    out.set_data(allocator::malloc(out.nbytes()));
+    return;
+  }
+
+  // Copy c into out and return
+  if (inputs[0].shape(-1) == 0) {
+    copy_gpu(
+        inputs[2],
+        out,
+        inputs[2].flags().row_contiguous ? CopyType::Vector : CopyType::General,
+        stream());
+    return;
+  }
+
   out.set_data(allocator::malloc(out.nbytes()));
   auto& s = stream();
   auto& d = metal::device(s.device);
diff --git a/mlx/ops.cpp b/mlx/ops.cpp
index e8c260425..922680110 100644
--- a/mlx/ops.cpp
+++ b/mlx/ops.cpp
@@ -472,6 +472,10 @@ array hadamard_transform(
     const array& a,
     std::optional<float> scale_ /* = std::nullopt */,
     StreamOrDevice s /* = {} */) {
+  if (a.size() == 0) {
+    throw std::invalid_argument(
+        "[hadamard_transform] Does not support empty arrays.");
+  }
   // Default to an orthonormal Hadamard matrix scaled by 1/sqrt(N)
   int n = a.ndim() > 0 ? a.shape(-1) : 1;
   float scale = scale_.has_value() ? *scale_ : 1.0f / std::sqrt(n);
@@ -4326,6 +4330,10 @@ array addmm(
 
     c = reshape(c, c_reshape, s);
   }
+  if (c.shape() != out_shape) {
+    throw std::invalid_argument(
+        "[addmm] input c must broadcast to the output shape");
+  }
 
   auto out = array(
       std::move(out_shape),
diff --git a/python/tests/test_blas.py b/python/tests/test_blas.py
index 6fca4885b..df459eadc 100644
--- a/python/tests/test_blas.py
+++ b/python/tests/test_blas.py
@@ -589,6 +589,10 @@ class TestBlas(mlx_tests.MLXTestCase):
         alpha = 0.5
         beta = 2.0
 
+        # c must broadcast to the output shape
+        with self.assertRaises(ValueError):
+            mx.addmm(mx.zeros((2, 2, 2)), mx.zeros((2, 2)), mx.zeros((2, 2)))
+
         # Regular batched case
         a_npy = np.random.normal(0.0, 1.0 / 128, (32, 128, 16)).astype(np.float32)
         b_npy = np.random.normal(0.0, 1.0 / 128, (32, 16, 16)).astype(np.float32)
@@ -745,6 +749,19 @@ class TestBlas(mlx_tests.MLXTestCase):
         mx.eval(c)
         self.assertEqual(c.shape, (0, 0))
 
+        c = mx.array(1.0, dtype=mx.float32)
+        a = mx.array([], dtype=mx.float32)
+        b = mx.array([], dtype=mx.float32)
+        out = mx.addmm(c, a, b)
+        self.assertEqual(out.item(), 1.0)
+        self.assertEqual(out.shape, ())
+
+        a = mx.zeros(shape=(5, 0))
+        b = mx.zeros(shape=(0, 5))
+        c = mx.random.uniform(shape=(5, 5))
+        out = mx.addmm(c, a, b)
+        self.assertTrue(mx.allclose(out, c))
+
     def test_block_masked_matmul(self):
         def ref_block_masked_mm(
             a, b, block_size, out_mask=None, lhs_mask=None, rhs_mask=None
diff --git a/python/tests/test_ops.py b/python/tests/test_ops.py
index d9e143d82..0921de788 100644
--- a/python/tests/test_ops.py
+++ b/python/tests/test_ops.py
@@ -2830,6 +2830,9 @@ class TestOps(mlx_tests.MLXTestCase):
         return H
 
     def test_hadamard(self):
+        with self.assertRaises(ValueError):
+            mx.hadamard_transform(mx.array([]))
+
         h28_str = """
         +------++----++-+--+-+--++--
         -+-----+++-----+-+--+-+--++-