Abstract :
Rosenfeld (A. Rosenfeld, A note on matrix quadratic residues, Amer. Math. Monthly 74 (1967) 804–811) considered the problem of how many solutions do there exist for 2×2 matrix equation: X2=A, over the prime fields of finite fields of characteristic different from 2. In this paper we will determine the square problem of 2×2 matrices and further we will find the number of solutions of 2×2 matrix equations: a1X12+a2X22+cdots, three dots, centered+amXm2=O, over finite fields of characteristic different from 2.
