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Question 41880: In the algebra of matrices why does there have to be a right and left distributive property?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! In the algebra of matrices why does there have to be a right and left distributive property?
BECAUSE MATRIX MULTIPLICATION IS NOT COMMUTATIVE.THAT IS
AB IS NOT EQUAL TO BA.CONSIDER THE FOLLOWING IN NORMAL ADDITION AND MULTIPLICATION
2+3=3+2...SO + IS COMMUTATIVE
2*3=3*2...SO * IS COMMUTATIVE
SO
2*(3+4)=2*3+2*4.....AND
(3+4)*2=3*2+3*4=2*3+2*4=2*(3+4)...HENCE HERE THERE IS NO NEED FOR LEFT AND RIGHT DISTRIBUTIVE PROPERTY...
BUT CONSIDER
2/3...IS NOT SAME AS 3/2
AND 2-3 IS NOT SAME 3-2
SO RIGHT AND LEFT SIDE OR RIGHT SIDE OPERATION IS IMPORTANT DIVISION OR SUBTRACTION ,BUT NOT IN ADDITION OR MULTIPLCATION
SIMILARLY IN CASEOF MATRICES
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