Ubuntu Networking :: Configuring Postfix Send And Receive Across Ethernet

I am would like to configure postfix to send and receive email across Ethernet (just for now). I have two machines with postfix installed both using Ubuntu 10.04 directly connected with an ethernet cable. I have successfully configured a machine to send email to gmail, however i have been unsuccessful in having these machines send email back and forth. I have been interested in setting up a little mail server at home and have just been trying some simple projects with postfix to start with. At this moment i am using ip addresses and am not concerned with using a dns server

machine A: has a fixed ip of 10.137.202.1, hostname = mail.me.com,
machine B: has a fixed ip of 10.137.202.20, hostname = mail.ubuntu.com
in the /etc/hosts file I map each hostname to ip address receptively (not sure if a good idea, but at this point I have been trying everything)

So I will execute from Machine B
echo "Here is a message" | mail -s 'Hello' cmd@[10.137.202.1]

I currently get from mail.log timed out while receiving the initial server greeting. I get from mail.err valid hostname or network address required in server description #[10.137.202.1]. Obviously when I run the mail command from cmd user i do not receive anything. I can receive mail from myself if from machine A, I sent an email using the command above. I would just like to send email from machine B and receive it on machine A via direct Ethernet connection. I have been through postfix documentation and have also read the postfix definitive guide and have had no luck.

Here is a recent main.cf as I have tried getting this to work (this is for machine A however, similar for B)

# Debian specific: Specifying a file name will cause the first
# line of that file to be used as the name. The Debian default
# is /etc/mailname.
myorigin = /etc/mailname .....