1. ## det

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

2. 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.)

3. Originally Posted by weasley74
if det(A)=1 what is det(-2A) ? shouldn't it be -2, or am I totally lost on this one?
$\displaystyle det(-2A)=(-2)^2det(A) \Rightarrow 4$

This assumes it is a 2x2 matrix. If it is a 3x3 matrix, then you need to take negative two to the third power and so forth...

EDIT: Not the first reply! Great explanation above!