Find the inverse elements for the permutations $(15643)$ and $(143)(256)$.
If $\sigma = (15643)$, then isn't $\sigma^{-1}=(34651)$? Since $(15643)\cdot(34651)=(15643)$?
Also for $(143)(256)$ the inverse would be $(652)(341)$ since $(143)(256) \cdot(652)(341)=(143)(256)?$
The inverse $\sigma^{-1}$ of $\sigma\in S_n$ is an element of $S_n$ such that $$\sigma^{-1}\sigma=\sigma\sigma^{-1}={\rm id}_{S_n}.$$
The inverse of a cycle $(s_1s_2\dots s_{m-1}s_m)$ is $$(s_ms_{m-1}\dots s_2s_1).$$ (Why?)
Hence $(15643)^{-1}=(34651)$ and $((143)(256))^{-1}=(256)^{-1}(143)^{-1}=(652)(341)$.