Öz In this article A will be a fixed n x n m atrix andxF (x) its m inim al polynom ial of degree m. The set of m atrices fj. (A), where f* (A) is a polynom ial, is an m-dimensional subspace of th e n 2 -dim ensional space of ali n x n m atrices [1]. The set of m atrices r^(A), where (fi ( x ) ,T (x)) - 1 and ff (x) = r. (x) (m o d Y (x) ) is a com m utative group under m atrix m ultiplication w hich is isom orphic to the group of polynom ials r^ (x) under m ultiplication modT* (x). W e also characterize properties of the m atrices f^ (A) in term s of properties of the polynom ials T (x).