Answer: does not matter.
References:
English4all
Grammar Girl
One of the shortest posts of all time! No, this is too short. Lets try another one.
Irregardless versus Regardless
Answer: regardless, because irregardless is not a word. This is elegantly pointed out several times in the 2006 cinematic masterpiece "Puff, Puff, Pass" by the character played by Danny Masterson.
Clarification
Irregardless is a nonstandard word. Meaning it is in the dictionary as common use, but not a proper word. Check out the Grammar Girl post on dictionary word usage stemming from the irregardless debate.