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Math Help - How do I show that adj(A) is invertible?

  1. #1
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    How do I show that adj(A) is invertible?

    The question I'm working on is basically this:

    If A is an invertible nxn matrix, show that adj(A) is also invertible and that:

    (adj A)^-1 = (1/detA) A = adj (A^-1)

    i've been able to prove their equality..

    but i don't know how to approach adj(A) is invertible..

    thanks.
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  2. #2
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    Quote Originally Posted by TabishX View Post
    The question I'm working on is basically this:

    If A is an invertible nxn matrix, show that adj(A) is also invertible and that:

    (adj A)^-1 = (1/detA) A = adj (A^-1)

    i've been able to prove their equality..

    but i don't know how to approach adj(A) is invertible..

    thanks.

    What equality were you able to prove?? Perhaps the basic one A\cdot Adj(A)=\det(A)\cdot I ?...but then we're done since:

    \left(A\det(A)^{-1}\right)Adj(A)=I\Longrightarrow the matrix Adj(A) is invertible and its inverse is \left(A\det(A)^{-1}\right) ...

    Tonio
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  3. #3
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    oh okay.. thank you..
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