Properties of Matrix Multiplication

  • 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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