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

If `A` is a square matrix of order 3 such that `|A|=5` , write the value of `|a d j\ A|` .

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To find the value of \(|\text{adj}\, A|\) for a square matrix \(A\) of order 3 with \(|A| = 5\), we can use the property of determinants related to the adjoint of a matrix. ### Step-by-step Solution: 1. **Understand the properties of determinants**: For any square matrix \(A\) of order \(n\), the determinant of the adjoint of \(A\) is given by the formula: \[ |\text{adj}\, A| = |A|^{n-1} \] ...
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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 :

    If A is a square matrix of order 3 such that |A|=3, then find the value of |adj(adjA)|

    If A is a square matrix of order nxxn such that |A|=lambda , then write the value of |-A| .

    If A is a square matrix of order 3 with |A|=9 , then write the value of |2.adj.A| .

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