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IF A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] th...

IF `A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}]` then show that `A^-1=A^3`.

Answer

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Knowledge Check

  • If A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] then A is

    A
    idempotent matrix
    B
    involutory matrix
    C
    nilpoten matrix of index2
    D
    nilpotent matrix of index 3

  • If A=[(1,-3,-4),(-1,3,4),(1,-3,-4)] then A^(2)=

    A
    `[(14,10),(-5,-1)]`
    B
    `[(-1,0),(0,-1)]`
    C
    `[(0,0),(0,0)]`
    D
    `[(0,0,0),(0,0,0),(0,0,0)]`

  • If A=[(1,3,3),(1,3,4),(1,4,3)] then A has

    A
    unique inverse
    B
    no inverse
    C
    two inverses
    D
    infinitely may inverses

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    If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)] , then show that A is hermitian matrix.

    IF A=[{:(2,-1,2),(1,3,-4):}] and B=[{:(1,-2),(-3,0),(5,4):}] then verify that (AB)'=B'A'.

    If A={:[(1,0,-2),(-2,-1,2),(3,4,1)]:} then A^(-1) =

    For the matrix A={:[(3,-3,4),(2,-3,4),(0,-1,1)]:}A^(-1)=

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