On most perfect magic squares of order four

A simple parametrization for 4x4 most perfect magic (MPM) squares is derived. This parametrization permits to calculate their powers and eigenvalues as well as their Moore-Penrose, group, and core inverses in an easy fashion. Such properties as EP-ness, normality, symmetry, and partial isometriness of the MPM squares are also characterized. Moreover, their eigenspaces are identified along with some properties of such squares with prime entries.