I seem to become confused whence computing simple cyclic notations as such.
From my understanding, the rule goes by starting from the right and to the left. However by doing this I only end up with (1), which i doubt since the answer is (23).
A hint or perhaps an explanation would be very helpful and much appreciated. Thanks
$(23)(1) = (1)(23)$ since the cycles are disjoint, and disjoint cycles commute.
$(23)(1)$ means $1$ maps to $1$, $2$ maps to $3$, and $3$ maps to $2$. When an element maps to itself, we can omit such a one-cycle, and it is implicitly understood that the missing element maps to itself.
So, the most brief way of denoting $(23)(1)$ is simply $(23)$.