Michael Sipser Edition 3 Exercise 1 Question 31 (Page No. 88)

Question

For any string $w = w_{1}w_{2} · · · w_{n},$ the reverse of $w,$ written $w^{R},$ is the string $w$ in reverse order$, w_{n} · · · w_{2}w_{1}.$ For any language $A,$ let  $A^{R} = \{w^{R}| w\in A\}.$ Show that if $A$ is regular$,$ so is $A^{R}.$