diff --git a/src/core/inverse.rs b/src/core/inverse.rs
index ed066e49..488c5b5b 100644
--- a/src/core/inverse.rs
+++ b/src/core/inverse.rs
@@ -45,18 +45,19 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
             match dim {
                 0 => true,
                 1 => {
-                    if relative_eq!(self.get_unchecked(0, 0), &N::zero()) {
+                    let determinant = self.get_unchecked(0, 0).clone();
+                    if determinant == N::zero() {
                         false
                     }
                     else {
-                        *self.get_unchecked_mut(0, 0) = N::one() / self.determinant();
+                        *self.get_unchecked_mut(0, 0) = N::one() / determinant;
                         true
                     }
                 },
                 2 => {
                     let determinant = self.determinant();
 
-                    if relative_eq!(&determinant, &N::zero()) {
+                    if determinant == N::zero() {
                         false
                     }
                     else {
@@ -94,7 +95,7 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
                                       m12 * minor_m11_m23 +
                                       m13 * minor_m11_m22;
 
-                    if relative_eq!(&determinant, &N::zero()) {
+                    if determinant == N::zero() {
                         false
                     }
                     else {
diff --git a/tests/matrix_inverse.rs b/tests/matrix_inverse.rs
index a37b54ff..fe1af112 100644
--- a/tests/matrix_inverse.rs
+++ b/tests/matrix_inverse.rs
@@ -61,3 +61,61 @@ fn matrix5_try_inverse() {
 
     assert_relative_eq!(a_inv, expected_inverse, max_relative=1e-4);
 }
+
+#[test]
+fn matrix1_try_inverse_scaled_identity() {
+    // A perfectly invertible matrix with
+    // very small coefficients
+    let a = Matrix1::new(1.0e-20);
+    let expected_inverse = Matrix1::new(1.0e20);
+    let a_inv = a.try_inverse().expect("Matrix is invertible");
+
+    assert_relative_eq!(a_inv, expected_inverse);
+}
+
+#[test]
+fn matrix2_try_inverse_scaled_identity() {
+    // A perfectly invertible matrix with
+    // very small coefficients
+    let a = Matrix2::new(1.0e-20,     0.0,
+                             0.0, 1.0e-20);
+    let expected_inverse = Matrix2::new(1.0e20,    0.0,
+                                           0.0, 1.0e20);
+    let a_inv = a.try_inverse().expect("Matrix is invertible");
+
+    assert_relative_eq!(a_inv, expected_inverse);
+}
+
+#[test]
+fn matrix3_try_inverse_scaled_identity() {
+    // A perfectly invertible matrix with
+    // very small coefficients
+    let a = Matrix3::new(1.0e-20,     0.0,     0.0,
+                             0.0, 1.0e-20,     0.0,
+                             0.0,     0.0, 1.0e-20);
+    let expected_inverse = Matrix3::new(1.0e20,    0.0,    0.0,
+                                           0.0, 1.0e20,    0.0,
+                                           0.0,    0.0, 1.0e20);
+    let a_inv = a.try_inverse().expect("Matrix is invertible");
+
+    assert_relative_eq!(a_inv, expected_inverse);
+}
+
+#[test]
+fn matrix5_try_inverse_scaled_identity() {
+    // A perfectly invertible matrix with
+    // very small coefficients
+    let a = Matrix5::new(1.0e-20,     0.0,     0.0,     0.0,     0.0,
+                             0.0, 1.0e-20,     0.0,     0.0,     0.0,
+                             0.0,     0.0, 1.0e-20,     0.0,     0.0,
+                             0.0,     0.0,     0.0, 1.0e-20,     0.0,
+                             0.0,     0.0,     0.0,     0.0, 1.0e-20);
+    let expected_inverse = Matrix5::new(1.0e+20,     0.0,     0.0,     0.0,     0.0,
+                                            0.0, 1.0e+20,     0.0,     0.0,     0.0,
+                                            0.0,     0.0, 1.0e+20,     0.0,     0.0,
+                                            0.0,     0.0,     0.0, 1.0e+20,     0.0,
+                                            0.0,     0.0,     0.0,     0.0, 1.0e+20);;
+    let a_inv = a.try_inverse().expect("Matrix is invertible");
+
+    assert_relative_eq!(a_inv, expected_inverse);
+}