toc regular language

Question

L=w(w^R)*        such that  w belongs to {a,b}* is regular ??? how?

Comments

I am trying..

w(w^R)* can have all the strings on (a,b)*. Because whatever be the string on (a,b) we take it as w and consider that 0 instances of (w^R)* has been taken. 

Eg: to check a string abbaba belongs to this L.

Here we say that w=abbaba and w^R=ababba. But we take epsilon for (w^R)*. So it becomes w.

So abbaba can belong to the language.

In this way all the strings on (a,b) can be considered as 'w' and w^R need not be taken.

So regular.

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ya this can be ...thank u