Routing Protocol - RIP Compatibility

In Tuesday ISMT218 lab session
I have try to setup two CISCO router using RIP routing protocol
RouterA and RouterB
RouterA use the default RIP version
RouterB use RIP version 2
At the beginning, i think that both of them cannot exchange information since they are using different version of the RIP protocol. However, I found that in the routing table, RouterA have a route to RouterB but RouterB doesn't have a route to RouterA.
I wondering even if they can communicate with each other, it should be RouterB have a route to RouterA, as RouterB using a newer version of RIP protocol. It may be a backward compatible in the RIP version 2, but I am wrong.
I have clean the dynamic route, and wait for 30 second for them to exchange routing information. After 30 second, the route appear again in the RouterA. oh, how come?!
After discuss with the TA, Mr. Bryan Man. I have turn on the RIP debug information on both router. Something interesting come out, both Router exchange their routing information, RouterA get it successfully and using it to build the routing table, but in RouterB, the one using RIP version 2, show that it have received the information, but since the version does not match, so it discard the message.
This is very funny that RIP protocol version2 does not have a backward compatibility, but is RIP version 1 have a "forward compatibility"?
I guess that RIP version 2 need more information to calculate and complete the routing table, since the routing information from version 1 cannot provide sufficient routing information for version 2, so it discard the information. However the routing information provided by version 2 is more than version 1 needed, so version 1 can still use for build the update the routing table.
I will examine my assumption later to see is it correct or not.
However, you are not suppose to have two different routing protocol, even same protocol with different version in the same network.