Postgresql – select something where date = “01/01/11”

I think you want to cast your dt to a date and fix the format of your date literal:

SELECT *
FROM table
WHERE dt::date="2011-01-01" -- This should be ISO-8601 format, YYYY-MM-DD

Or the standard version:

SELECT *
FROM table
WHERE CAST(dt AS DATE) = '2011-01-01' -- This should be ISO-8601 format, YYYY-MM-DD

The extract function doesn’t understand “date” and it returns a number.