void inversion(double **A, int N)
{
    double temp;
    double **E = new double *[N];
    for (int i = 0; i < N; i++)
        E[i] = new double [N];
 
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
        {
            E[i][j] = 0.0;
            if (i == j)
                E[i][j] = 1.0;
        }
    for (int k = 0; k < N; k++)
    {
        temp = A[k][k];
        for (int j = 0; j < N; j++)
        {
            A[k][j] /= temp;
            E[k][j] /= temp;
        }
        for (int i = k + 1; i < N; i++)
        {
            temp = A[i][k];
            for (int j = 0; j < N; j++)
            {
                A[i][j] -= A[k][j] * temp;
                E[i][j] -= E[k][j] * temp;
            }
        }
    }
    for (int k = N - 1; k > 0; k--)
    {
        for (int i = k - 1; i >= 0; i--)
        {
            temp = A[i][k];
            for (int j = 0; j < N; j++)
            {
                A[i][j] -= A[k][j] * temp;
                E[i][j] -= E[k][j] * temp;
            }
        }
    }
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            A[i][j] = E[i][j];
 
    for (int i = 0; i < N; i++)
        delete [] E[i];
    delete [] E;
}