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Explain why matrix multiplication is not commutative.

  1. Nov 13, 2013 #1
    The title says it all.

    Commutative* sorry
    Mod note: fixed title.
    Last edited by a moderator: Nov 13, 2013
  2. jcsd
  3. Nov 13, 2013 #2


    Staff: Mentor

    Why do you want to know?
  4. Nov 13, 2013 #3
    Let A = [aij] and B = [ajk] where j ≠ k, then AB is defined, but BA is not.

    But consider the case where i = j = k, so that A = [ai] and B = [ai] are square matrices.

    Then, take for example i = 2 and calculate AB and BA. What do you find?

    Generally, AB ≠ BA, for all values of i. It just stems from the definition of matrix multiplication.
  5. Nov 13, 2013 #4


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Matrix multiplication is defined only for certain rectangular matrices A and B. The matrix product AB is defined only if the number of columns in A is equal to the number of rows in B. Assuming this condition is met, the product AB is defined, but the product BA may not be.
  6. Nov 13, 2013 #5


    Staff: Mentor

    h6ss and SteamKing,
    Please hold off further comments until I can ascertain whether this is a homework question. If it is, it was posted in the wrong section with no efforts shown.
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