Show that the multiplicative group $\mathbb{Z}_{10}^{\times}$ is isomorphic to the additive group $\mathbb{Z}_4$. Show that the multiplicative group $\mathbb{Z}_{10}^{\times}$ is isomorphic to the additive group $\mathbb{Z}_4$.
I'm completely lost with this one.

write down all the elements of $\mathbb{Z}^{\times}_{10}$ explicitly. any find a generator by its Cayley Table or by explicit calculation. Now map this generator to $1$ in $\mathbb{Z}_4$.
