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If A is a non-singular matrix then prove...

If A is a non-singular matrix then prove that `A^(-1) = (adjA)/(|A|)`.

Text Solution

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The correct Answer is:
`=> A ^(-1) = (AdjA)/( det A )`
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Knowledge Check

  • If A is a nonsingular matrix, then detA^(-1)=

    A
    `(detA)^(n-2)A`
    B
    `detA`
    C
    `1/(detA)`
    D
    `(Adj)A`

  • If A is a singular matrix then adj A is

    A
    singular
    B
    nonsingular
    C
    symmetric
    D
    not defined

  • If is a nonsingular matrix of type n then Adj(AdjA)=

    A
    `(detA)^(n-2)A`
    B
    `detA`
    C
    `1/(detA)`
    D
    `(Adj)A`

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    If A is a nonsingular matrix of type n Adj(AdjA)=kA , then k=

    If A is a nonsingular matrix and B is a matrix, then detB=

    Suppose n gt 1 and A is a n xx n non singular matrix such that |Adj A| = |Adj (Adj A)|. Then the matrix whose rank is n, is

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