Checking regularity of a given language.

Question

$L =\left \{ w(w^{R})^{*}: w\in(a,b)^{*} \right \}.$

Is this language regular?

Answer 1

$w(w^R)^* = w \cup w(w^R) U w(w^R)^2 ………....$   where w is (a,b)*

so as in the language w is coming which belongs to (a,b)* so it will cover all strings over a and b so it is regular language