One of the most important properties of the FFT (Fast Fourier Transform) algorithm is that we can use it to compute the IFFT. This is a common exercise in DSP (Digital Signal Processing) courses. So, in case you are here just for the code (MATLAB), there you go;

function [x_n]=ivfft(X_k) x_n=conj(fft(conj(X_k)))/(max(size(X_k)));

The rest of you who are interested in the proof, stick with me.