Finding the inverse of divisor functions in terms of $\mu$

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How would I find the inverse of $τ(n)=\sum_{d|n}1$ and $\sigma(n)=\sum_{d|n}d$ in terms of $\mu$? Where $µ$ is the Mobius function.

So I know $τ=u*u$ and $\sigma=N*u$ and also $u*\mu=I$ but I cant quite see how to get to the final steps.

I know I need to show that $τ^{-1}=\mu*\mu$ but can't quite see how to get to this step?

I think $\sigma^{-1}=N*\mu$ is that right?