I want to put these images in the RowSelector column depending upon these states:
inactive/not selected - nothing
inactive/selected - check mark
active/not selected - triangle
active/selected - check mark and triangle
How can this be done (preferably through the properties, in code if not).
This documentation article titled, "Styling Row Selector Images for Different States of a Row" would get you started on how to use your images in the row selectors.
http://help.infragistics.com/NetAdvantage/WinForms/2010.3/CLR2.0/?page=WinGrid_Styling_Row_Selector_Images_for_Different_States_of_a_Row.html
Then you'll need to take a look at your requirements to see what events you want to wire up to (e.g. InitializeRow, AfterExitEditMode, etc). The InitializeRow event would be used to get those intial selectors set up, and then events like AfterExitEditMode would give you the opportunity to update the selector image if the proper change took place.
I can see how that might apply to an active row that is either selected or not-select, but how does it do anything for an inactive row? I do not see any image attributes for rows that are not active.