Insert date based on cell contents?

Hi all,

I'm looking for a little help if possible, please. I'm putting together a spreadsheet to help with my caseload at work. I'm wanting to know if it's possible please to have a cell insert the current date based on an action from another cell:

For instance: Cell A2 has data validation if option 'open' is chosen it will enter today's date into cell C2. Alternatively, if Cell A2 is set to 'closed' it will leave the date inside C2 and then update D2 to the current date?

I've included a copy of my Excel document should you require it? Test.xlsx

Any help or assistance you can provide would be greatly appreciated.

Metrix :-)