Abstract
This study is about multiplication of matrices. Multiplication of real numbers, which can be written along a line, is also two way. Here, the direction is not an influential factor even when the elements are switched. For example $3.2=6$ and $2.3=6. $ In matrices this makes left and right multiplication is mandatory. Left multiplication is already defined. This is multiplication in known matrices. Left multiplication is used in the studies since the definition of this operation until today. The most insurmountable situation here is that matrices do not commutative Property according to this operation. The left product is taken into account, when $AB $ is written. Here the matrix $A$ is made to be effective. This left product is denoted by $AB. $ The right definition in this study is denoted by $\underleftarrow{AB}. $ This operation multiplication is seen to be compatible with the left multiplication. The commutativity property in matrices is reinvestigated with this approach. The relation between the right multiplication and the Cracovian Product is given by J. Koci´nski (2004).
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