MunyaM Having an agent set as admin just gives them access to the Admin panel, it doesn't actually affect ticket permissions at all (although with admin access an agent could set their own permissions to whatever they wanted!).
Permission to close tickets is defined via roles - for the affected agent(s) check the role in Admin -> Agents -> Agents -> [agent name] -> Access ensuring you verify the role for the relevant department.
The permissions for each role can be verified in Admin -> Agents -> Roles. Here, ensure the role assigned to each department has the close tickets permission.