 If r represent scalar elements and A, B and C represent matrices:

A(BC) = (AB)C—————————Associative property
shows that the order in which matrices are multiplied can be disregarded 
A(B+C) = AB+AC
shows that matrices obey distributive properties when the matrix A is being multiplied from the left side 
(B+C)A = BA +CA
 shows that matrices obey distributive properties when the matrix A is being multiplied from the right side
 Example
 r(AB) = (rA)B = A(rB)
 shows that when matrices are being multiplied by a scalar element, the order in which multiplication takes place can be disregarded
 Example
 IA = A = AI
 shows that when a matrix is multiplied by the indentity matrix, the product is the same as the original matrix
 Example
AB≠BA ——matrix multiplication Is NOT commutative
http://www.math.nyu.edu/~neylon/linalgfall04/project1/dj/propofmatrixmult.htm
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