关于二阶实矩阵的一个问题

A Problem Concerning Real Matrices of Order Two

设n是正整数,A是二阶实矩阵.该文证明了:如果An=E2且│A-E2│=n,其中E2是二阶单位矩阵,则必有n=3,A=(abc-1-a),其中a、b、c是适合a2+a+bc+1=0的实数.

Let n be a positive integer and let A be real matrix of order two. In this paper we prove that if A^n= E2 and ｜A - E2 ｜ = n, where E2 is the unit matrix of order two, then n = 3 and A = （^a c ^b -1-a）, where a,b,c arerealnumberswith a^2＋a＋bc＋1=0 .