data validation case sensitive string in google sheets

I'm trying to formulate a data validation code in Google Sheets for a simple 6 letter string - any 3 capital letters and any 3 lowercase letters. I believe I should be using the RegexMatch function? Here's what I tried:

=RegexMatch("[A-Z][A-Z][A-Z]\[a-z][a-z][a-z]")

But when I try to type AAAaaa in the cell it rejects it.