Necessary and Sufficient Conditions for two Matrices to Hold Multiplicative Property

Let A≠ uI; u is a positive integer, is a square matrix of order n; n= 2 or 3 over a finite field fq ; q is prime. The set G ={A | ;|A|≠0} forms the group under matrix multiplication. Let 0(N(A) denote the order of N(A), where N(A), is the normalizer of A in G . Here in this paper we find all matrices which commute with under matrix multiplication. we also discuss determination of N(A) in G over fq and computation of 0(N(A) in G over Fq.