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`" For the matrix A and identity matrix "I," if "AB=BA=I" then that matrix "B" is inverse matrix and "A" is invertible "A^-1=`

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For the matrix A and identity matrix I if AB=BA=I then that matrix B is inverse matrix and A is invertible (AB)^(-1)=

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Knowledge Check

  • The matrix having the same matrix as its inverse

    A
    `[[1, 1, 1], [1, 1, 1], [1, 1, 1]]`
    B
    `[[1, 0, 1], [0, 1, 0], [0, 0, 1]]`
    C
    `[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`
    D
    `[[0, 1, 0], [1, 1, 1], [0, 1, 0]]`

  • If A is an invertible matrix and B is a matrix, then

    A
    rank (AB) = rank (A)
    B
    rank (AB) = rank (B)
    C
    rank (AB) gt rank (A)
    D
    rank (AB) gt rank (B)

  • A is a square matrix and I is an identity matrix of the same order. If A^(3)=O , then inverse of matrix (I-A) is

    A
    `I+A`
    B
    `I-A+A^(2)`
    C
    `A+A^(2)`
    D
    `I+A+A^(2)`

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