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Math Help - Proving that matrices commute

  1. #1
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    Proving that matrices commute

    a) A, B and C are n x n matrices such that AB= I and CA = I.

    show that B = C.

    b) A and B are n x n matrices that commute

    i) show that A^2 and B^2 commute.
    ii) Give a generalization of this result.
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  2. #2
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    Quote Originally Posted by swiftshift View Post
    a) A, B and C are n x n matrices such that AB= I and CA = I.

    show that B = C.

    b) A and B are n x n matrices that commute

    i) show that A^2 and B^2 commute.
    ii) Give a generalization of this result.
    I'll address b (i). Write AABB. Do you see how to manipulate that to obtain BBAA, using what we've been given?
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  3. #3
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    AB=I
    Multiply left C*:
    CAB=C
    (CA)B=C
    as CA=I
    we get B=C.
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