--- a/mlx/linalg.cpp
+++ b/mlx/linalg.cpp
@@ -806,11 +806,16 @@
 
   // Small-matrix fast path
   if (n <= 3) {
-    auto raw = det_raw_small(input, s);
-    auto abs_raw = abs(raw, s);
-    auto sgn = sign(raw, s);
-    auto logabs = log(abs_raw, s);
-    return std::make_pair(sgn, logabs);
+    if (n <= 1) {
+      auto raw = det_raw_small(input, s);
+      return std::make_pair(sign(raw, s), log(abs(raw, s), s));
+    }
+    auto row_scale = stop_gradient(max(abs(input, s), -1, true, s), s);
+    row_scale = where(equal(row_scale, array(0, dtype), s),
+                      array(1, dtype), row_scale, s);
+    auto raw = det_raw_small(divide(input, row_scale, s), s);
+    auto log_scale = sum(log(squeeze(row_scale, -1, s), s), -1, false, s);
+    return std::make_pair(sign(raw, s), add(log(abs(raw, s), s), log_scale, s));
   }
 
   // General LU-based path