Making a Button stay depressed in a DataGridView

I want a button called "Edit" in the first column of my DataGridView which will signify that the row is being edited, and no other row can be edited as they display in a color showing read only mode.  When the user clicks Edit for another row, my dialog will verify the data's okay in the row just edited, and make that button no longer depressed.  Only one Edit button can be depressed at a time.

How do I handle this inside a DataGridView?  The button is of type DataGridViewDisableButtonColumn() and is working fine within the DataGridView, but I need to add this new behaviour and am not quite sure where to add it.

Thanks!