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Given A and B are two non-singular matri...

Given A and B are two non-singular matrix such that `B ne I, A^(5)=I` and `AB^(2)=BA`, then the least value of n for which `B^(n)=I` is :

A

63

B

64

C

31

D

32

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let A and B are two non - singular matrices such that AB=BA^(2),B^(4)=I and A^(k)=I , then k can be equal to

    A
    5
    B
    10
    C
    15
    D
    16

  • If A,B are two n xx n non-singular matrices, then

    A
    AB is non-singular
    B
    AB is singular
    C
    `(AB)^(-1)=A^(-1)B^(-1)`
    D
    `(AB)^(-1)` does not exist

  • Let A and B be two non-singular square matrices such that B ne I and AB^(2)=BA . If A^(3)-B^(-1)A^(3)B^(n) , then value of n is

    A
    `4`
    B
    `5`
    C
    `8`
    D
    `7`

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    Suppose A and B are two non-singular matrices of order n such that AB=BA^(2) and B^(5)=I ,then which of the following is correct

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