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If A and adj A are non-singular square m...

If A and adj A are non-singular square matrices of order n, then adj `(A^(-1))=`

A

`(adj A)^(T)`

B

`adj (adj (A))`

C

`1/|A| A`

D

`|A|*A`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • If A is a non-singular matrix of order n, then A(adj A)=

    A
    `A`
    B
    `I`
    C
    `|A|I_n`
    D
    `|A|^(2)I_n`

  • If A is a non-singular matrix of order nxxn, then : |adj*A|=

    A
    `|A|^(n)`
    B
    `|A|^(n-1)`
    C
    `|A|^(n-2)`
    D
    `n|A|`

  • If A and B are non - singular matrices of order three such that adj(AB)=[(1,1,1),(1,alpha, 1),(1,1,alpha)] and |B^(2)adjA|=alpha^(2)+3alpha-8 , then the value of alpha is equal to

    A
    `(9)/(5)`
    B
    `(8)/(5)`
    C
    3
    D
    2

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