Thank you for your replies about Mathew Rickard.
@GrahamSimons
Thank you, I checked out that link. It said there were some online records at the findmypast website. I subscribed (one week free trial) and I searched for him there. I didn't find anything. I suppose the next step is to visit Kew, or pay someone to search for me.
Thanks for the tip about NCOs, I had no idea if this is a difficult or easy search. It seems to be possible that there are no records.
@ShaunJ
Thanks for looking.
@Ashtone Thanks for that, I actually have it already. After Wexford he was in Dublin and then Killarney Asylum. I have a lot of info after 1842, but almost nothing from before 1842. Apart from a bakery 1837-1839, I have nothing. His estimated birth year is 1808, so he could have been in the army any time from say 1826 to 1837. I cannot find any birth record, or anything at all, before 1837.
In case anyone searches, there was a Mathias Rickard who was a baker in Dublin 1795-1830. He was the father of this Mathew Rickard. Actually this Mathew is really named Mathias, I think, but he seems to often be Mathew.