EIGRP Authentication

It is ridiculously easy. Yes, Right! But there's some point I wanna highlight.
IP Addressing :
--------------------
R1 - s0/0.12 point-to-point = 131.1.12.1/24 ; lo1 = 1.1.1.1/8
R2 - s0/0.21 point-to-point = 131.1.12.2/24 ; lo1 = 2.2.2.2/8

Configure EIGRP Authentication on R1
------------------------------------------------
!
key chain EIGRP
key 1
key-string ABC
key 2
key-string cisco
!
!
interface Serial0/0.12 point-to-point
ip address 131.1.12.1 255.255.255.0
ip authentication mode eigrp 100 md5
ip authentication key-chain eigrp 100 EIGRP
frame-relay interface-dlci 102
!


Configure EIGRP Authentication on R2
------------------------------------------------
!
key chain EIGRP
key 1
key-string DEF
key 2
key-string cisco
!
!
interface Serial0/0.21 point-to-point
ip address 131.1.12.2 255.255.255.0
ip authentication mode eigrp 100 md5
ip authentication key-chain eigrp 100 EIGRP
frame-relay interface-dlci 201
!
!

According to the above configuration, will R1 and R2 form EIGRP neighbors? Umm...May be Yes..May be No...I thought that EIGRP neighbor will form even though key-strings of key1 do not match, but key-strings of key2, of R1 and R2, are still match. Unfortunately, I was wrong. R1 and R2 totally cannot form neighbor with above configuration.
It will form the neighbor relationships when key-strings of key1 do match, even though key-strings of key2 doesn't match. Oh Yeah, It's Not A Big Deal! But, what if we face that question in Open Ended Section. :)