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If A is a square matrix of order n xx n ...

If A is a square matrix of order `n xx n` and k is a scalar, then `adj (kA)` is equal to (1) `k adj A` (2) `k^n adj A` (3) `k^(n-1) adj A` (4) `k^(n+1) adj A`

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Knowledge Check

  • If A is a square matrix of order nxxn and k is a scalar, then adj(kA)=

    A
    k adj A
    B
    `k^(n)adj A`
    C
    `k^(n-1)adj.A`
    D
    `k^(n+1)adjA`

  • If A is a square matrix of order n, then |adj A|=

    A
    `|A|^(n-1)`
    B
    `|A|^(n-2)`
    C
    `|A|^(n)`
    D
    none

  • If A is a square matrix of order n, then det (adj A)=

    A
    `(det A)^(n-1)`
    B
    (det A)^(n-2)
    C
    `(det A)^(n)`
    D
    None of these

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