Abstract
In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided features is discussed under which conditions. These features have been determined. Examples are given for features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.
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