Proving $(a + ab)^*a = a(a + ba)^*$ Need to prove $(a + ab)^*a = a(a + ba)^*$ by using regular algebra.
Concatenation does not commute. So repeated use of commutativity will fail. I am getting confused about which identity I should use to prove this. What I can interpret is that I just need to change the side of $a$ but the $^*$ must be kept outside. But I am not able to do this.
Any help will be appreciated.
This is an instance of the identity $(xy)^*x = x(yx)^*$ with $x = a$ and $y = 1 + b$:
$$
(a + ab)^* a = (a(1+b))^*a = a((1+b)a)^* = a(a +ba)^*
$$