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Matrix proof!

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    if T is an invertible matrix, and A=(T^-1)B*T, prove that det B = det A


    2. Relevant equations

    A(BC) = (AB)C


    3. The attempt at a solution
    im not certain if inverse T and T will cancel to 1
    A=B
    det A = det B
     
  2. jcsd
  3. Apr 27, 2010 #2
    What do you know of the determinant of the product of matrices and of the determinant of inverses? Use those facts and the proof should be immediate.
     
  4. Apr 28, 2010 #3
    oh would be it
    det(A) = det(T^-1)det(BT)?
     
  5. Apr 28, 2010 #4
    Yes, but continue further.
     
  6. Apr 28, 2010 #5
    oh alright, i think i got it.
    det(A) = det(B)det(T)^-1det(T)
    det(A) = det(B)

    thanks for the help!
     
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