Question 41880
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