Parent Child Domain (Windows 2003)

I have Parent Child Domain Scenario. Domain A.com(Parent) and Domain B.A.Com. I know the trust are transitve and I should be able to authenticate via kerberos. However here is my delima. If I try to browse to shares on resources in the Parent domain logged in as a administrator from the Child domain it ask for credentials from the parent domain to access the resource. If I am logged in as the administrator of the parent domain and I try and browse resources in the child domain it works without asking for credentials. If the trust are transitive then why doesn't this work both ways?