Is the Determinant of a Covariant Tensor of Order 2 an Invariant of Weight 2?

[anotherann]

Question: Let Aij denote an absolute covariant tensor of order 2. Show that the determinant A = det(Aij ) is an invariant of weight 2 and A is an invariant of weight 1.

I have little clue about this question. Would writting down the transformation rule from barred to unbarred 2nd-order tensor work? Any help would be greatly appreciated! Thanks!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Question: Let Aij denote an absolute covariant tensor of order 2. Show that the determinant A = det(Aij ) is an invariant of weight 2 and A is an invariant of weight 1.

This makes no sense- "Show that A is an invariant of weight 2" and "A is an invariant of weight 1".

I have little clue about this question. Would writting down the transformation rule from barred to unbarred 2nd-order tensor work? Any help would be greatly appreciated! Thanks!

Homework Statement

Homework Equations

The Attempt at a Solution

What are the definitions of "invariant of weight 2" and "invariant of weight 1"?

 

[antarctic]

The determinant of a (0,2) tensor is a tensor density of weight 2. See, for example, page 41 of Tensors, Differential Forms, and Variational Principles by Lovelock and Rund.