Question

if det(A) = -1 Then what does det (2A) equal?

Answer 1

Create a matrix where its determinant is -1. Then take that same matrix and multiply it by two, then find its determinant.

Answer 2

can it be a 2 x 2 matrix ?

Answer 3

Well, the problem here is, that your result will depend on the dimensions of the matrix. If you can't figure out the general rule, try a 2x2 and a 3x3. Maybe don't use "2" as your scalar but just write it out for any scalar c.. it'll become obvious, what det(cA) has to be ;)

Answer 4

that should be -2

Answer 5

NO, it is not -2. As I stated before, it does depend on the size of the matrix. It is -4 for a 2x2 and -8 for a 3x3.. The general rule is: \[\det(cA) = c^n \det(A)\]for a nxn Matrix.

I normally just don't state the solution. However, if people give advice that's just plain wrong, I fear the asker might be mislead.

(velossahonda - I would elaborate, why it's like that if you are still interested?? )