Question

How to prove that the determinant of the metric in lorentz transformation is 1?

Answer 1

Answer:

I have been asked to prove that the determinant of any matrix representing a Lorentz transformation is plus or minus 1

Answer 2

Answer:

Consider a matrix transformation T that acts on a vector x:

x′=Tx

.

Now, I know that one-dimensional linear transformations expand the length by a factor |det(T)|, two-dimensional linear transformations expand the area by a factor |det(T)|, and three-dimensional linear transformations expand the volume by a factor |det(T)|.

How can I see this mathematically though? I was thinking of calculating the norm ||x′||=||T||⋅||x|| but don't know how to deal with