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## Homework Statement

Given a N-dimensional manifold, let g

_{ab}, be a metric tensor.

Compute

(i) g

_{ab}g

^{bc}

(ii)g

_{ab}g

^{ab}

Also, just need a clarification on something similar.

g

^{cd}T

_{cd}=g

^{cd}T

_{dc}=tr T?

I'm pretty sure its yes. Probably even a stupid question but a clarification would be useful.

## Homework Equations

## The Attempt at a Solution

(i)tr g ?

(ii)Here I'm caught between tr g, since I'm thinking its still the tensor and its inverse, and the indices don't matter.

The other option is g

_{a}

^{c}.

Which is correct?