I read that the Rubik's Cube is a permutation group. Here, it says that "Neutral Element - *there is a permutation which doesn't rearrange the set: ex. $RR'$ *" (For Rubik's Cube notations see this.)
I know that for some mathematical structure, say $(S, \ast)$, the identity element is defined as $a\ast e = e \ast a = a$ where $e$ is the identity element $\forall\:a \in S$ and that $e$ is unique. For a Rubik's Cube, how is the identity element unique? For $D$, we have $D'$. For $F$ we have $F'$ and so on.
The identity element is simply doing nothing to the Rubik's Cube. If you indexed every face on the cube, doing nothing to the cube would result in the identity permutation where nothing changes.