You are being asked to perform filtering in the Fourier domain. When multiplying spectra, you will have to account for the cost of multiplying complex numbers; you can assume they require 4
MACs, since (x + i y)(z + i w) = (xz-yw) + i (xw+yz).The cost of the FFT is noted in the problem statement for part h. This cost is in MACs; i.e., I've already accounted for any costs associated with handling complex numbers for that component of the problem.
You need to estimate the cost of taking just the FFT of the "reflection-augmented" image. No other filtering costs are to be considered.
Slide 14 of the first image processing lecture makes the case that the DFT treats the input signal as periodic by putting repeated copies of the finite length input sequence next to each other, repeating the copies across the real line. In 2D, the DFT assumes the input image is repeated by tiling it in x and y, repeating copies across the plane. This assumption affects the results of convolution perfomed by multiplying DFT spectra.
You are asked to develop a test to determine whether an orthogonal matrix is a rotation matrix or a reflection matrix. It should be noted that reflection matrices are not restricted to the "canonical" reflections that simply negate one of the diagonal elements of an identity matrix. In general, a reflection transformation will mirror objects across some plane through the origin and can be written as matrix products involving canonical reflection and general rotation, yielding a matrix for which all entries can be non-zero. The key is to think in terms of the mirroring behavior of reflections vs. the non-mirroring behavior of rotations.