The unidirectional scattering of electromagnetic waves in the backward and forward direction, termed Kerkers' first and second conditions, respectively, is a prominent feature of sub-wavelength particles, which also has been found recently in all-dielectric metasurfaces. Here we formulate the exact polarizability requirements necessary to achieve both Kerker conditions simultaneously with dipole terms only and demonstrate its equivalence to so-called "invisible metasurfaces". We further describe the perfect absorption mechanism in all-dielectric metasurfaces through development of an extended Kerker formalism. The phenomena of both invisibility and perfect absorption is shown in a 2D hexagonal array of cylindrical resonators, where only the resonator height is modified to switch between the two states. The developed framework provides critical insight into the range of scattering response possible with all-dielectric metasurfaces, providing a methodology for studying exotic electromagnetic phenomena.