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Rank of adjugate matrix

  1. Aug 23, 2012 #1
    how that the rank of the adjugate matrix (r(adj(A))) is :

    n if r(A)=n

    1 if r(A)=n-1

    0 if r(A)<n-1

    How to deal with the proof? Can someone give more insight? What proof should I use here?

    I have an idea only for the third statement.
  2. jcsd
  3. Aug 23, 2012 #2
    What is [itex]A\cdot adj(A)[/itex]?? What are the implications on the rank?
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