Michael Sipser Edition 3 Exercise 1 Question 67 (Page No. 93)

Question

Let the rotational closure of language $A$ be $RC(A) = \{yx| xy ∈ A\}.$

1. Show that for any language $A,$ we have $RC(A) = RC(RC(A)).$
2. Show that the class of regular languages is closed under rotational closure.