Does the sum of all tensor invariants have any meaning or application?

Question

I have come across a formula with multiple tensors. After some modification, I ended up with the sum of all the invariants of one of the tensors. E.g., if it was a tensor $A$ with $3\times 3$ matrix representation, I'd have

$${\rm tr}(A) + \frac{1}{2}\left(({\rm tr}A)^2 - {\rm tr}(A^2)\right) + \det(A)$$

Now, I wonder whether this has some more general context. Is this a special property of some object, a solution to some equation, or did it occur to any of you in any way?

Thanks for any hints.

Answer 1

Isn't this just $1-{}$the characteristic polynomial evaluated at $-1$, or $\det{(A+I)}-1$?