Question

Prove that If B is invertible, then det(B^-1*A*B)=det(A). Thanks for any help :)

Answer 1

Do you know any rules of determinants?

Answer 2

how about if you have two matrices G and H then:

det(GH)=det(G)*det(H)

Answer 3

Is it equal to the identity matrix?

Answer 4

I mean...det(B^-1AB)=det(B-1)det(A)det(B)=Det(A)*I=det(A)

Answer 5

is det(B-1)*det(B)=I?

Answer 6

@Kainui

Answer 7

Well luckily we can show this quite easily! Check this out! \[\LARGE 1=\det(I)=\det(BB^{-1})=\det(B)\det(B^{-1})\]

Answer 8

YAY!! Thankyou :)