Trustee can be anyone that you both trust

Legally, either A or B can be the trustee, I believe unless there is law in your state specifically barring it. However, it is not advisable to construct the transaction this way. The trustee should have no affiliation with either party and will have the legal authority and responsibility to take care of the property according to local laws and trust agreement. If he is at fault or being gross negligent, he can be sued by the beneficiary for breach of fiduciary duty and/or fiduciary care. Therefore, normally people would not want to assume such job unless get reasonably compensated.