Question

can anyone help me with proof that det(A)=det(-A) for nxn matrices?

Answer 1

You can find it in any Linear Algebra book

Answer 2

ok I guess I'll look harder

Answer 3

Which Linear Algebra book are you refering?

Answer 4

I know we are using the scaling method three times which gives us det(B)=s(det(A))

Answer 5

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

Answer 6

so does -1(det(A)=det(-A)

Answer 7

ahh yes...I get it now, I overlooked that formula, the exponent threw me off, thakns

Answer 8

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