I recommend writing out the matrix corresponding to this for n=2 and 3. That should give you an idea of the pattern.
I still don't get it. Can you help me with n=3 for example. Thank you so much!
Let T: R^n -> R^n be defined by
T(z1, z2, ... , zn) = (z2-z1, z3-z2, ... , z1-zn)
What is T*, is T invertible and what are che characteristic and minimal polynomials of T?