How do I add a column to datagridview through code?

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C#

I have added database table data to DataGridView in the C# Windows application form. I want to add one more column to it with Edit Button in each row. How can I do it with code?

What I have tried:

public Form1()
       {
           InitializeComponent();
           SqlConnection con = new SqlConnection(@"Server= DESKTOP-AK4NH6J\SQLEXPRESS;Database=Interview;Trusted_connection=True");
           con.Open();
           SqlCommand cmd = new SqlCommand("select * from Person", con);
           SqlDataAdapter da = new SqlDataAdapter(cmd);
           DataTable dt = new DataTable();
           da.Fill(dt);
           dt.Columns.Add("Edit", typeof(string));
           con.Close();
           dataGridView1.DataSource = dt;
       }