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Question about Determinants

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose A is a square matrix of size n. When is det(-A) = -det(A)?

    2. Relevant equations

    N/A

    3. The attempt at a solution

    My approach to the problem is to simply multiply the size n identity matrix by -1, then multiplied by A. For example: det((-1)*IdentityMatrix[n]*A) = det((-1)*IdentityMatrix[n])*det(A). At this point I could answer the original question by saying this is true when n is odd. But I get the impression I am overlooking some other very obvious answer or condition, and am wondering if anyone can think of a different approach. Thanks.
     
  2. jcsd
  3. Nov 14, 2009 #2

    lanedance

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    Homework Helper

    you reasoning seems sound to me...
     
  4. Nov 14, 2009 #3
    Looks good to me too.

    Remember that for scalar c and matrix A, det(cA)=cndet(A) where n is the size of A. Plugging in c = -1 gives your answer.
     
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