gsl_matrix *
invert_a_matrix(gsl_matrix *matrix)
{
    gsl_permutation *p = gsl_permutation_alloc(size);
    int s;

    // Compute the LU decomposition of this matrix
    gsl_linalg_LU_decomp(matrix, p, &s);

    // Compute the  inverse of the LU decomposition
    gsl_matrix *inv = gsl_matrix_alloc(size, size);
    gsl_linalg_LU_invert(matrix, p, inv);

    gsl_permutation_free(p);

    return inv;
}