Is this Matrix a Tensor, Pseudotensor, or Neither?

[Marthius]

I am having trouble understanding how to tell if a matrix is a tensor, a pseudo tensor or neither or the above.
Given this matrix
\begin{vmatrix}2x^-2y^2 & 4xy\\ 4xy & -2x^2+2y^2\end{vmatrix}
I thought of trying just inverting the components and checking the sign, but I don't think that this will tell me if it is actually a tensor.

 

[Landau]

Can you give your definition of 'tensor' and 'pseudo tensor'?

 

[Marthius]

Actualy I don't think I can, that may be part of the issue.