Question

A: nxn, and B=s^-1 AS (for some nonsingular nxn matrix s). Prove that det(A)=det(B)...

Answer 1

Matrixes :D

You do know that the determinant of the product of matrices is the product of of their determinants, right? :)

Answer 2

yes

Answer 3

Also that given a non-singular matrix, the determinant of its inverse is the reciprocal of its determinant?

Answer 4

yeah....so if the det is a scalar quantity.. I can rearrange the order as well?

Answer 5

if so, peace of cake

Answer 6

Yep :)
Multiplication is just that :D

Answer 7

cool thanks peter!

Answer 8

OkayOkay :D
Anytime :)

Answer 9

For the proof to be correct tho...do you first consider A to be nonsingular or you don't have to?

Answer 10

You don't :)
It doesn't matter, does it?
If A is singular, its determinant is zero, and that's that :)
also, if A is singular, then
det(s)det(A)det(s^-1)
= det(s)(0)det(s^-1) = 0
So it will still hold :)

Answer 11

yeah, okay. a little derpy this fine morning.