Datagridview And Down Arrow To Move Down Rows?

With a two column Datagridview, first column with a number in it, and second column with nonwrap text. When the datagridview width is less than the width of the data in the two columns, the only way I can get a horizontal scrollbar to show is with the width set for both columns. If I then try to scroll down the rows using the down arrow, the grid jumps to show only the second column. I have tried various settings for the columns - fill - fillweight - autosize etc.

I found one solution, setting the first column to frozen in the key down event and then setting it back in the key up event but the scrollbar does flicker and I am sure this is not the correct way to do this.

The user needs to scroll down the rows and be able see the first column whilst doing this and then if necessary scroll right to read any text not visible.