if det(A)=1 what is det(-2A) ? shouldn't it be -2, or am I totally lost on this one?

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- Mar 3rd 2008, 08:59 AM #1

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- Mar 3rd 2008, 09:06 AM #2

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I believe this is what you need to know:

If a is a constant and A an n×n square matrix, then |aA|=a^n|A|.

Thus, $\displaystyle det(-2A) = (-2)^n \times det(A)$. So it depends on the size of your matrix - if it's, say, a 2 x 2 matrix, then

$\displaystyle det(-2A) = (-2)^2 \times det(A) = 4 \times 1 = 4$.

Make sure to use the size of your matrix for n.

(This is result 11 here: Determinant -- from Wolfram MathWorld. I actually don't recall this particular result, so there may be another method, particularly if you don't know the size of the matrix.)

- Mar 3rd 2008, 09:37 AM #3