Is the permutation in $S_1$ even or odd?

Question

A permutation is even or odd depending on whether it can be written as an even or odd number of transpositions. However, the permutation in $S_1$ cannot be written as a product of transpositions, so is it just undefined?

Answer 1

It can be written as the product of $0$ transpositions, and $0$ is an even number, making it an even permutation. This is not just true of the permutation in $S_1$, it's true of the identity element in every symmetric group $S_n$.

Answer 2

Hint: Since zero is even, what can we conclude?