Inverse system of sinc? I'm doing some self-study for an important exam I'll have in late March and came across the following question:

So, using the convolution properties, if I want to find an identity system so that the final output is just the input, I would need one of the following, right?

h(t) * h'(t) = $\delta(t)$

H(w) * H'(w) = 1, so H'(z) = $\frac{1}{H(z)}$


My question is, if we go through option 2, then we are going to have a bunch of 1/0 since the Fourier Transform of the sinc will be a rect, so the system would not be stable.
Also, the sinc function itself is not invertible as we have many points that maps to 0 and the even symmetry of the function.
So does that means that for this particular case it is impossible to get such an identity system?
Thanks for the help!
Your $h(t)$ is an ideal low pass filter with cutoff frequency of $75$ Hertz. At the output, everything above $75$ Hertz will be gone and equal to zero. If you're thinking about the inverse system, you need to think about getting back the original input. What can you say about the original input signal at frequencies greater than $75$ Hertz? Isn't it anybody's guess as to what used to be there?