How to make two way communication between DataGridView and ArrayList?

Question

C++ / C#

Hello, please tell me, there is a task:

To sort an array and search for an element, use the methods of the ArrayList class. To manipulate the contents of an array, it is mandatory to use a two-way relationship with the DataGridView.

How to make two-way communication?

// Клик по пункты "Создать => ввод"
        private void вводToolStripMenuItem_Click(object sender, EventArgs e)
        {
            ArrayList list = new ArrayList();
            dataGridView1.Visible = true;
            dataGridView1.AutoGenerateColumns = true;
            dataGridView1.DataSource = list;
        }

I do like this, but it's dataGridView1empty and I can't add new values ​​there, see form screenshot below

Thanks in advance for your reply.