anonymous
  • anonymous
can anyone help me with proof that det(A)=det(-A) for nxn matrices?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
You can find it in any Linear Algebra book
anonymous
  • anonymous
ok I guess I'll look harder
anonymous
  • anonymous
Which Linear Algebra book are you refering?

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anonymous
  • anonymous
I know we are using the scaling method three times which gives us det(B)=s(det(A))
nowhereman
  • nowhereman
you can find all you need here: http://en.wikipedia.org/wiki/Determinant Just use \[\det (αA) = α^n \det (A) \] and you will see your conjecture does only hold for even numbers n
anonymous
  • anonymous
so does -1(det(A)=det(-A)
anonymous
  • anonymous
ahh yes...I get it now, I overlooked that formula, the exponent threw me off, thakns
anonymous
  • anonymous
there are many ways to prove it, depends on how the determinant is defined. In beginning linear algebra book, the determinant is not defined using the Leibniz formula. In that case, there is another proof

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