| Summary: | This research will discuss about the generalized inverse product of
matrices over field � . Generalized inverse of matrices is generalization of inverse
matrices. Inverse matrices can be searched on a non singular square matrices
while the existence of generalized inverse matrices is guaranteed for any matrix.
Inverse matrices and generalized invers of matrices can be found in many way.
Similarly, to find the inverse product of matrices and generalized inverse product
of matrices. Suppose A and B in non singular matrices the invers product of
matrices AB is the multiplication from each of the inverse matrix B and A .
However, if A and B are rectangular matrices the multiplication from each of
generalized inverse matrix B and A is not always a generalized inverse matrix
multiplication AB .
Let �S,�� is semigroups. Element a�S is regular if there exist element
x�S such that a � axa . Also S is regular if each of it�s elemen is regular. Let S is
regular and a,b�E�S � is all idempoten elemen in S . Sandwich set of a,b�E�S �
defined as S �a,b� � �c� E �S � ca � bc � c dan acb � ab� .
In this research, the sandwich set method will be used to find the
generalized inverse product of matrices through the formation of regular semigrup
R� A� and L� A� each which is the set all of multiplication between matrices with
it�s generalized inverse from the right and left view matrices matrices
multiplication with a regular semigrup. Furthermore these methods will compared
with the methods that is used by Setiadji and Zekraoui that specifically discuss
about generalized inverse of matrices over complex numbers � and real numbers
� .
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