Given a tensor Mab, Prove that its trace is a scalar.
The Attempt at a Solution
To prove the trace is a scalar, I know I have to prove it doesn't transform under coordinate transformations.
Now, we can transform M^a_b as follows.
For the trace Maa, the transformation is as follows. I've used the Kronecker delta for changing Mab to Maa. ( Am I along the right lines in doing so?).
Then I thought using the delta I change dxb to dxa and cancel the two dxa. However that would then the delta away from Mab, leaving it as Mab as before rather than Maa.
That's the best I can do, please help.