modular arithmetic - How to calculate $2 ^ {-1} pmod{10}$

I want to know how to compute the inverse of a number when the module is composite and the number is not coprime.

Can anyone give me the options with an example of how to compute with $2 ^ {-1} \pmod{10}$?

Is there a way to do factorisation or some similar technique that ends with the same result like: $1/9 \pmod{10} = 1/3 \times 1/3 \pmod{10}$ and because 3 is comprime of 10 then is possible?

Thanks