So this is a follow-on question to my other question (Can we make a non-regular language regular via concatentation?).
Given the following,
$L = \{0^n1^m2^m \mid n>1, m>1\}$
$A = \{0^n \mid n>1\}$
$B = \{1^m2^m \mid m>1\}$
Is $L$ in fact just $A$ and $B$ concatenated (I believe it is, but I want to verify that)?
Further, does proving $B$ non-regular prove that $L$ is non-regular since they don't share characters?