Discrete Maths - Permutation

Question

Let $A = \{ 1,2,3,4,5,6 \}$ and $p = (1,2,4)$ be a permutation of $A$. Compute $p^2$. Please help me with this question. I totally have no idea how to do it.

Answer 1

$(124)(124)$ You read this notation from right to left. Any element that doesn't appear is a fixed-point of the permutation, so $p(1)=1,p(3)=3$, etc.

Now going from right to left, we see $4 \to 1 \to 2$ and $2 \to 4 \to 1$. See if you can do it for the last number, $1$.

EDIT- Actually I think its better to see this when you have two different cycles

say $(214)(124)$, then $4 \to 1 \to 4$, $2 \to 4 \to 2$, and $1 \to 2 \to 1$. So for this example,

$$(214)(124) = (1)(2)(4) = Id$$