Is it normal to not have a relationship with your brother?

Ok, I'm 25 and my brother is 22 and we don't get along at all, I find that he is very inconsiderate and selfish and needs to grow up. He and I used to get along when we were younger, I'm older and I admit I did some things, ie took advantage of him, like beat him up and stuff nothing serious just the occasional lash here or hit there, say he did something when it was really me, u know stuff like that, I apologised about those things in a letter to him that he refused to read and I tried to be nice to him and stuff but he just has all that in the back of his mind and doesn't want to let it go. Now that we have gotten older, I would expect that he would get over it and move on, but now he uses that as the excuse to do what he wants, he breaks into my room, steals stuff from my mother and me, wants to yell at my mother, basically make our life a living hell and my mother blames me for those things, I'm at the point now that I have nothing to say to him, not even a goodmorning and my mother is of the opinion that if I talk to him, his attitude would change and the living in the house would be good, because families are not to be like that. What I want to know is am I wrong for not wanting to have anything to do with him or should I try and talk with him and hope that it would change, because I am really tired or being the one that is blamed when he does his stupidness and I'm tired of hearing that it is my fault that my brother gets on the way that he does, thank you.