# Trouble understanding the proofs in Marion and Thorton

## Homework Statement

I am having trouble understanding the proofs in Marion and Thorton [Newest Edition]. The section where he goes through proof of products in tensor notation. An example is page 26 example 1.6. I don't get the switching of the indices on the very last part. Also can someone prove to me that $$\vec{A}\times \vec{B}=-\vec{b}\times \vec{A}$$ using tensor summation notation. Want to make sure I am doing it right.