Calculation of inverse impulse response in the frequency domain
Your result is correct, even if it seems a bit counterintuitive. Note that you don't compute the Fourier transform but the discrete Fourier transform (DFT). The system you want to invert has the impulse response
$$g[n]=\frac12\delta[n-19]\tag{1}$$
Obviously, the inverse system must advance the incoming signal by $19$ samples:
$$g_{inv}[n]=2\delta[n+19]\tag{2}$$
Clearly, that system is non-causal. Taking into account the implicit periodicity of the DFT (and IDFT) with length $N=100$, the signal $g_{inv}[n]$ cannot be distinguished from a signal $g_{k,inv}[n]=g_{inv}[n+kN]$, $k\in\mathbb{Z}$. Your result is just $g_{-1,inv}[n]$:
$$g_{-1,inv}=2\delta[n+19-N]=2\delta[n-81]\tag{3}$$