Show that the language L $\{(,)\}$such that L consists of all strings

of balanced parentheses is not regular. For example $-()$and $(()())$ in L$,$but

$()))/$in L$.$You must NOT use the pumping lemma $($hint $-$use closure properties$).$

Hi$,$I need help with this problem, please show and explain your solution clearly. I will upvote, thanks in advance!