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I've spent 6 hours, still can't get it.

  1. May 17, 2005 #1
    B is a n*n matrix

    1. Let B^2 =B. Prove that either det(B) =1 or B is singular.
    2. If Transpose(B) = B^-1 , what is det(B)?
     
  2. jcsd
  3. May 17, 2005 #2

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    If b^2=b, then det(b^2)=det(b)^2=det(b), which has two solutions for det(b). For the second part, since a singular matrix doesn't have an inverse, you are forced into the only allowed non-zero determinant.
     
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