Research identifies conditions for matrices to commute under multiplication in finite fields, suggesting foundational properties in algebra.
AbstractLet 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.
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Anu Kathuria (2025) studied this question.
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