Is it normal that i can't trust my brother?

He has lied about me on several occasions to family and friends saying that I treat him like garbage and that I sell drugs. He once stole my television and sofa from my apartment when my friends and I were outside at a barbecue and I had to steal it back. He stole my girlfriend(she was a controlling bitch, but it's not right he did it). He "borrowed" my car, crashed it, and left the scene. He's a pretentious brat around my friends. He's always begging our family for money, stooping so low as to bother our teenage sister. He's manipulative, can't hold down a job and lives with our aunt. I am in the process of purchasing my first house and he's begging to live with me. I told him no and my family is nagging me and putting me down for not letting him live with me. He lied to them and told them i beat him up. I already know what's going to happen if I let him. My family knows he's a jobless mooch, and yet they keep handing him stuff. He's 22 and refuses to do anything for himself. is it normal I don't trust him? Should I let him live with me to shut my family up?