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$L2$ is Regular ot not.?Please give proper example.

$L_1= \{a^nb^n  \mid  n\geq 0 \} $

$L_2 = (L_1)^*$
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Basic: A language is not regular Language if you need an extra Data structure for keeping track of alphabet.

Here the same problem: 

In L1, we need to keep track of 'a' so that you can compare with a number of 'b'. So L1 is not regular Language. 

 Similarly, in L2 = { a^nb^n,  a^nb^na^nb^n, ............}.   here we also need to compare a number of 'a' and 'b'. So, L2 is also not a regular language.

If anything not clear, please comment, I try to simplify more.

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