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Need some help on a proof

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data
    1) If A is a product of elementary matrices, show that det(adj(A))=(det(A))^(n-1)
    2) Prove the above statement without the assumption on A


    2. Relevant equations
    Hmm... Know A*adj(A)=det(A)*In (i.e. the n by n identity matrix)



    3. The attempt at a solution
    Well I know the assumption implies the use of the equivalent theorems for invertible matrices...not sure how to set this up though. Have to show A as a n by n matrix in order to thoroughly prove it, but seems to get complicated quickly if trying to evaluate the adj(A)...
    Anyone clue me in on this?
     
  2. jcsd
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