Please write the following proofs in a logically complete yet concise manner. Do not leave out or skip any logical steps. Example of similar proof provided: emulate it and its structure.

$1)$ Prove the language L is not regular, over the alphabet $\backslash$Sigma $=\{$a$,$ b$\}.$ L $=\{$ aib$2$i : i $>0\}$

$2)$ Prove the language M is not regular, over the alphabet $\backslash$Sigma $=\{$a$,$ b$\}.$ M $=\{$ wwR : w is an element of $\backslash$Sigma $*$ i$.$e$.$ w is any string, and wR means the string w written in reverse$\}.$ In other words, language M is even$-$length palindromes.