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Math Help - [SOLVED] Diagonalization question 2

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    [SOLVED] Diagonalization question 2

    Let A and B be unkown diagonalizable matrices. If A and B have exactly the same eigenvectors as each other, then show that AB = BA.
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  2. #2
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    Quote Originally Posted by jkeatin View Post
    Let A and B be unkown diagonalizable matrices. If A and B have exactly the same eigenvectors as each other, then show that AB = BA.
    A=P_1^{-1}D_1P_1, \ \ B=P_2^{-1}D_2P_2, where D_1,D_2 are diagonal and P_1,P_2 are matrices with the eigenvectors of A,B as their columns repectively. so P_1=P_2 and since diagonal matrices commute

    with each other, we'll have: AB=P_1^{-1}D_1D_2P_1^{-1}=P_1^{-1}D_2D_1P_1=BA. \ \Box
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    ok i got ya, thanks for the help man
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