Dr. Najmaddin Hama Gareb

Department of Mathematics, School of Science Education, University of Sulaimani

Abstract

This work is divided into two parts; first we find all matrices which commutative with any given

matrix, and second devoted to some multiplication commutative properties of M2x2(F), where F is a

field. Moreover some cases which the ring M2x2(F) become commutative are studied.

Keywords: Multiplication commutative of two by two matrices over a field F.

References

[1] Kolman B. and David R., Elementary Linear Algebra, 7th Edition, 2000, prentice-Hall,

New Jersey.

[2] Nielsen H.A. , Elementary Commutative Algebra, 2005, Department of Mathematical

Sciences-University of Aarhus.

[3] Artin M. , Algebra, 1991, Prentice-Hall, Printed in India by Anand Sons.

[4] Drazin, M. P.; Dungey, J. W.; Gruenberg, K. W. , Some Theorems on Commutative

Matrices, 1951, J. London Math. Soc. 26 (3): 221–228, doi:10.1112/j1ms/s1-26.3.221.

[5] Suprunenko D. and Tyshkevich R., Commutative Matrices, Translated by Scripta

Technica, Inc, 1968, Academic Press New York and London.

[6] Feit, W. and Fine, N. J., Pairs of Commuting Matrices over Finite Field, 1960, Duke

Math. J. 27, No.1, 91-94.

[7] Hamburger, H.L., A Theorem on Commutative Matrices, 1949, J. London Math, Soc. 24,

200-206.