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If A is a square matrix of order 3 such ...

If `A` is a square matrix of order `3` such that `|A|=3` , then find the value of `|a d j(a d jA)|`

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To find the value of \(|\text{adj}(\text{adj} A)|\) given that \(|A| = 3\) for a \(3 \times 3\) matrix \(A\), we can use the properties of determinants and adjoints. ### Step-by-Step Solution: 1. **Understand the properties of the adjoint**: For any square matrix \(A\) of order \(n\), the determinant of the adjoint of \(A\) can be expressed as: \[ |\text{adj}(A)| = |A|^{n-1} \] ...
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Knowledge Check

  • If A is any square matrix of order 3xx3 such that |A|=3 , then the value of |adjA| is ?

    A
    3
    B
    `(1)/(3)`
    C
    9
    D
    27
  • If A is any square matrix of order 3xx3 such that |A|=3 , then the value of |adjA| is ?

    A
    3
    B
    `(1)/(3)`
    C
    9
    D
    27
  • If A is a square matrix of order 3 such that |A|=5 , then |Adj(4A)|=

    A
    `5^(3)xx4^(2)`
    B
    `5^(2)xx4^(3)`
    C
    `5^(2)xx16^(3)`
    D
    `5^(3)xx16^(2)`
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    If A is a square matrix of order 3 such that |adjA|=64 , then the value of |A| is :

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