V članku karakteriziramo obrnljive marike nad poljubnim komutativnim antikolobarjem ▫$S$▫ z 1 in poiščemo strukturo grupe ▫$GL_n(S)$▫. Poiščemo tevilo nilpotentnih matrik nad celim, komutativnim, ...končnim antikolobarjem. Dokažemo, da se lahko vsaka nilpotentna ▫$n \times n$▫ matrika nad celim antikolobarjem zapiše kot vsota ▫$\lceil \log_2n \rceil$▫ matrik, katerih kvadrat je enak 0, in poiščemo potrebno število sumandov s kvadratom enakim 0, da se lahko poljubna matrika s sledjo 0 zapiše kot njihova vsota.
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