diff --git a/Eigen/src/LU/InverseImpl.h b/Eigen/src/LU/InverseImpl.h
index 1bab00c01..27e263945 100644
--- a/Eigen/src/LU/InverseImpl.h
+++ b/Eigen/src/LU/InverseImpl.h
@@ -77,10 +77,11 @@ inline void compute_inverse_size2_helper(
     const MatrixType& matrix, const typename ResultType::Scalar& invdet,
     ResultType& result)
 {
+  typename ResultType::Scalar temp = matrix.coeff(0,0);
   result.coeffRef(0,0) =  matrix.coeff(1,1) * invdet;
   result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
   result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
-  result.coeffRef(1,1) =  matrix.coeff(0,0) * invdet;
+  result.coeffRef(1,1) =  temp * invdet;
 }
 
 template<typename MatrixType, typename ResultType>
@@ -165,7 +166,12 @@ struct compute_inverse<MatrixType, ResultType, 3>
     cofactors_col0.coeffRef(2) =  cofactor_3x3<MatrixType,2,0>(matrix);
     const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
     const Scalar invdet = Scalar(1) / det;
-    compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
+    if(extract_data(matrix) != extract_data(result)) {
+      compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
+    } else {
+      MatrixType matrix_t = matrix;
+      compute_inverse_size3_helper(matrix_t, invdet, cofactors_col0, result);
+    }
   }
 };
 
@@ -191,7 +197,12 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
     invertible = abs(determinant) > absDeterminantThreshold;
     if(!invertible) return;
     const Scalar invdet = Scalar(1) / determinant;
-    compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
+    if(extract_data(matrix) != extract_data(inverse)) {
+      compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
+    } else {
+      MatrixType matrix_t = matrix;
+      compute_inverse_size3_helper(matrix_t, invdet, cofactors_col0, inverse);
+    }
   }
 };
 
@@ -273,7 +284,13 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
     using std::abs;
     determinant = matrix.determinant();
     invertible = abs(determinant) > absDeterminantThreshold;
-    if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
+    if(invertible && extract_data(matrix) != extract_data(inverse)) {
+      compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
+    }
+    else if(invertible) {
+      MatrixType matrix_t = matrix;
+      compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse);
+    }
   }
 };
 
@@ -347,6 +364,8 @@ inline const Inverse<Derived> MatrixBase<Derived>::inverse() const
   *
   * This is only for fixed-size square matrices of size up to 4x4.
   *
+  * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
+  *
   * \param inverse Reference to the matrix in which to store the inverse.
   * \param determinant Reference to the variable in which to store the determinant.
   * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
@@ -387,6 +406,8 @@ inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
   *
   * This is only for fixed-size square matrices of size up to 4x4.
   *
+  * Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
+  *
   * \param inverse Reference to the matrix in which to store the inverse.
   * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
   * \param absDeterminantThreshold Optional parameter controlling the invertibility check.