
Tensor Algebra question
I am working on my homework for a class, and I am really stuck
the question I was given was:
prove that S(a ⊗ b) = (Sa) ⊗ b
Does anyone have any tips on how to solve this?
For further explanation this is problem 6a from this book on the page the link goes to
sorry I should have elaborated further. S is suppose to be a tensor map while a and b are supposed to be vectors
upon further looking at the book, it looks like a linear map. But I guess what they were just trying to get across is that it is a Tensor. such that v = Su. The hint in the back of the book says apply each side of the identity to an arbitrary vector v.

Definition:
$\displaystyle
(a \otimes b)v=(bv)a
$
$\displaystyle
(ST)v=S(Tv)
$
$\displaystyle
S(a \otimes b)v=S \: ( \: (a \otimes b)v \:)=S \: ( \: (bv)a \: )=(bv) \: Sa
$
$\displaystyle
( \: (Sa )\otimes b \: ) \: v= \: (bv)Sa
$

thanks a lot that did the trick!