diff --git a/tests/python/unittest/test_operator.py b/tests/python/unittest/test_operator.py
index ee94629485c8..7fbdd1ef1319 100644
--- a/tests/python/unittest/test_operator.py
+++ b/tests/python/unittest/test_operator.py
@@ -6444,8 +6444,13 @@ def test_laop_6():
         check_numeric_gradient(sym, location, numeric_eps=num_eps, rtol=rtol_bw,
                                atol=atol_bw, dtype=dtype)
 
-    a = np.sqrt(np.arange(4 * 4)).reshape(4, 4)
+    ## det(I + dot(v, v.T)) = 1 + dot(v.T, v) >= 1, so it's always invertible;
+    ## det is away from zero, so the value of logdet is stable
+    v = np.random.random(4)
+    a = np.eye(4) + np.outer(v, v)
     a = np.tile(a, (3, 1, 1))
+
+    # test matrix inverse
     r = np.eye(4)
     r = np.tile(r, (3, 1, 1))
     test_inverse = mx.sym.linalg.inverse(data)
@@ -6453,6 +6458,23 @@ def test_laop_6():
     check_fw(test_eye, [a], [r])
     check_grad(test_inverse, [a])
 
+    # test matrix determinant
+    # det
+    r = np.linalg.det(a)
+    test_det = mx.sym.linalg.det(data)
+    check_fw(test_det, [a], [r])
+    check_grad(test_det, [a])
+    # logdet
+    r = np.log(np.linalg.det(a))
+    test_logdet = mx.sym.linalg.logdet(data)
+    check_fw(test_logdet, [a], [r])
+    check_grad(test_logdet, [a])
+    # test slogdet
+    r = np.log(np.abs(np.linalg.det(a)))
+    _, test_slogdet = mx.sym.linalg.slogdet(data)
+    check_fw(test_slogdet, [a], [r])
+    check_grad(test_slogdet, [a])
+
 @with_seed()
 def test_stack():
     for _ in range(100):