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Thread: why algebraic rules wont work for nxn matrices?

  1. #1
    DrZ
    DrZ is offline
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    why algebraic rules wont work for nxn matrices?

    explain why each of the following algebraic rules will not work in general when the real numbers a and b are replaced by nxn matrices A and B.

    a) (a + b)^2 = a^2 +2ab + b^2
    b) (a + b) (a - b) = a^2 - b^2

    for a) I think the reason is because AB does not equal BA so 2ab makes no sense


    But for b) I feel like its the same reason.

    if you FOIL it with A and B matrices you get
    AA -AB +BA -BB

    So it again doesn't make sense with matrices since

    (A+B)(A-B) doesn't equal (A-B)(A+B)

    is this right?
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by DrZ View Post
    is this right?
    Yes.
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