how do you calculate the following determinant: det((-2B^T)^-3)) when det(B)=5

Question

amistre64 · Answer

since the determinant doesnt care if its Ted or not; B^T = 5

the ^-3 might have me concerned tho

amistre64 · Answer

anonymous · Answer

ok thanks

amistre64 · Answer

its still that ^-3 thats got me a little concerned; you sure you typed it correctly?

anonymous · Answer

yeah that means that its 1/(-2B^t)^3 but i dunno where to go from there. like if there's a property to help or smthg

amistre64 · Answer

det(AB) = det(A) det(B)  if A and B are the same size

anonymous · Answer

okayy but what do you do when the determinant is to the 3rd power?

amistre64 · Answer

wht does the third power mean?

anonymous · Answer

like 2nd power is squared, third power....

anonymous · Answer

cubed

amistre64 · Answer

well, we know the thrm for det(AB) is just multiplications ... are powers multiplications?

anonymous · Answer

well its a multiplication by itself. so the determinant multiplied by itself 3 times

amistre64 · Answer

id say so yes.

that should be all the thrms we need to solve it them

anonymous · Answer

aightosss amigosssssss danke freund :)

amistre64 · Answer

bitteshun .. if i recall me duetch

$$\frac{1}{(-2*5)^3}$$

anonymous · Answer

right so what do u do after that? is it like 1/ (-2)^3*5^3

anonymous · Answer

btw ur deutsch is fantabolical

zarkon · Answer

what is the size of B

anonymous · Answer

its a n3X3

amistre64 · Answer

ja ...meine grossmutter sint duetch

zarkon · Answer

that matters

anonymous · Answer

how so?

zarkon · Answer

$$Det(cA)=c^nDet(A)$$

when $A$ is an $n\times n$ matrix

amistre64 · Answer

thrm 1 ....yeah

zarkon · Answer

missed your link  :)

anonymous · Answer

omgooshhh thanks :) i could kiss you right now