How to do FullColumn Selection on a DataGridView with SelectioMode set to CellSelect

Question

Good evening.
I am working on a winForm where I need to use DataGridView control to display data read from a user supplied txt file with no pre-knowledge of how it is formatted but using delimiters which will be supplied by the user(students). I set the datagridview's (dgView) SelectionMode to CellSelect and handle the ColumnHeaders_MouseClick event to provide the option for fullColumn Select as shown below:
private void dgView_ColumnHeaderMouseClick(object sender, DataGridViewCellMouseEventArgs e)
{
for each(DataGridViewRow row in dgView.Rows
{
dgView. Columns[e.ColumnIndex].Selected = true;
}
}
Now the problem is that when I check the dgView. SelectedColumns.Count it gives me zero(0) meaning that no Column was selected. please how do I get around this?
thanks.