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If A is a nilpotent matrix of index 2, t...

If `A` is a nilpotent matrix of index 2, then for any positive integer `n ,A(I+A)^n` is equal to `A^(-1)` b. `A` c. `A^n` d. `I_n`

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Knowledge Check

  • If A is a square matrix such that |A| = 2 , then for any positive integer n, |A^(n)| is equal to

    A
    `2^(n)`
    B
    `n^(2)`
    C
    0
    D
    2n

  • For a positive integer n, what is the value of i^(4n+1) ?

    A
    1
    B
    `-1`
    C
    It is parallel to the y-axis
    D
    `-i`

  • If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the vlau of (I_(n+1)-I_(-1)) is,

    A
    1
    B
    2
    C
    `pi//4`
    D
    `pi`

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