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If A and B are square matrices of the same order such that AB=Ba , then prove by inducation that `AB^(n)=B^(n)A`. Further , prove that `(AB)^(n)=A^(n)B^(n)` for all `n in N`.

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Knowledge Check

  • If A and B are symmetric matrices of same order , then AB +BA is a ……

    A
    skew symetric matrix
    B
    symmetric matrix
    C
    Zero matrix
    D
    identify matrix

  • If A and B are matrices of same order , then (AB'-BA') is a ………….

    A
    skew symmetric matrix
    B
    null matrix
    C
    symmetric matrix
    D
    unit matrix

  • If A and B are square matrices of same order then (A^(-1)BA)^(n) = ………… , n inN .

    A
    `A^(-n)B^(n)A^(n)`
    B
    `A^(n)B^(n)A^(-n)`
    C
    `A^(-1)B^(n)A`
    D
    `n(A^(-1)BA)`

    • Similar Questions

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