diff --git a/mpmath/matrices/linalg.py b/mpmath/matrices/linalg.py
index 2e9503cc..a6a3571e 100644
--- a/mpmath/matrices/linalg.py
+++ b/mpmath/matrices/linalg.py
@@ -134,6 +134,9 @@ class LinearAlgebraMethods:
                 if current > biggest: # TODO: what if equal?
                     biggest = current
                     p[j] = k
+            # without pivot LU fails
+            if p[j] is None:
+                raise ZeroDivisionError('matrix is numerically singular')
             # swap rows according to p
             ctx.swap_row(A, j, p[j])
             if ctx.absmin(A[j,j]) <= tol:
@@ -539,8 +542,6 @@ class LinearAlgebraMethods:
         try:
             # do not overwrite A
             A = ctx.matrix(A).copy()
-            if any(all(ctx.almosteq(0, x) for x in A[:, c]) for c in range(A.cols)):
-                return 0 * A[0, 0]
             # use LU factorization to calculate determinant
             try:
                 R, p = ctx.LU_decomp(A)
diff --git a/mpmath/tests/test_linalg.py b/mpmath/tests/test_linalg.py
index 86e92c3d..b9dc72a9 100644
--- a/mpmath/tests/test_linalg.py
+++ b/mpmath/tests/test_linalg.py
@@ -69,10 +69,15 @@ A10 = matrix([[1.0 + 1.0j, 2.0, 2.0],
             [4.0, 5.0, 6.0],
             [7.0, 8.0, 9.0]])
 b10 = [1.0, 1.0 + 1.0j, 1.0]
+
 A11 = matrix([[4, 0, -2],
              [2, 0, -4],
              [2, 0, 5.5]])
 
+A12 = matrix([[1,0,0],
+              [0,1,0],
+              [0,0,1.0j]])
+
 
 def test_LU_decomp():
     A = A3.copy()
@@ -96,6 +101,12 @@ def test_LU_decomp():
     LU_decomp(A, overwrite=1)
     assert A != bak
 
+    try:
+        LU_decomp(A11)
+        assert False
+    except ZeroDivisionError:
+        assert True
+
 def test_inverse():
     for A in [A1, A2, A5]:
         inv = inverse(A)
@@ -197,7 +208,7 @@ def test_det():
     assert round(det(A6)) == 78356463
     assert det(zeros(3)) == 0
     assert det(A11) == 0
-
+    assert absmin(det(A12*1e-30) - 1e-30) < eps
 
 def test_cond():
     A = matrix([[1.2969, 0.8648], [0.2161, 0.1441]])