Winform dataGridView cells proble - winforms

Question

I have a DataGridView in a Winform desktop project in net 6.0
This DataGridView's generic row is composed by a DataGridViewCheckBoxCell in the first column, and another 6 DataGridViewTextBoxCells in the subsequent columns : the first one of the DataGridViewTextBOxCell (column 1) is permanently ReadOnly.
What I want to do is make the Cells from the second TextBox to the last one (that is columns 2 to 6) ReadOnly when the CheckBox is unchecked, and restore them to ReadWrite when the checkbox is checked.
What I do is override the dataGridViev.CellClick event, and when the sender is the element in column 0 (the checkbox) I get the row index and I iterate on the cells of the row from index 2 to 6 and set the ReadOnly property to true or false depending on the state of the checkobx itself.
The mechanism basically works fine, I read the event on the exact column/row, I correctly get the state of the checkobox (maybe in a not-so-smart way...) : but when it comes to setting the ReadOnly property I can see that ,in spite of iterating on the 2 to 6 column, it skips the cell in column 2 and sets the one in column 1 instead: all the settings on the other columns work correctly. I thought it was a matter of configuring the columns in the designer but all the columns from 2 to 6 are set identically.
My event handler is the following :
private void dataGridView1_CellClick(object sender, DataGridViewCellEventArgs e)
{
if (e.ColumnIndex == 0) // if checkbox
{
int row = e.RowIndex;
bool setState = true;
DataGridViewCheckBoxCell check = (DataGridViewCheckBoxCell)(dataGridView1.Rows[row].Cells[0]);
if (check.Value != null && check.Value == "true")
{
setState = true;
check.Value = "false";// CheckState.Unchecked;
}
else
{
setState = false;
check.Value = "true";// CheckState.Checked;
}
for (int i = 2; i < dataGridView1.Rows[row].Cells.Count; i++)
{
DataGridViewTextBoxCell txt = (DataGridViewTextBoxCell)(dataGridView1.Rows[row].Cells[i]);
txt.ReadOnly = setState;
if (setState) txt.Style.BackColor = Color.Gray;
else txt.Style.BackColor = Color.White;
}
}
}