MacBook Air help to identify which replacement keyboard is needed?

Hi Guys, I have a problem with a late 2010 11" MacBook Air which may be water damaged by the previous owner.

I am getting the exact same behavior as AndrewP described in his thread:

Intermittent shutdown: overheat or keyboard short?

"I have a late 2010 MBA which occasionally pops up a dialog box asking "if I want to shut down" then turns off by itself"

After reading the thread I suspect I need a new keyboard and think I can do the keyboard rivet/screw replacement rather than buying the entire top unit.

But I can't seem to identify exactly which keyboard I need to get. Can someone advise?

I measured the MBA screen and its a bit over 11" diagonally, definitely not a 13". The serial number on Apple's checker returns "MacBook Air (11-inch Late 2010)". The last 4 of the serial number is DDQY.

But the model printed on the bottom of the MBA says A1369, and according to Google this seems to be the model number for a 13" MBA. Is there something weird going on?

Are there a few different model numbers that will interchange keyboards without problems? Which keyboard should I get?

Any help is appreciated. Thanks.