Solving Symmetric Tensor: c\cdot (A \times b) \neq (A \times b) \cdot c

[germana2006]

Homework Statement

Demostrate:
c\cdot (A \times b) \neq (A \times b) \cdot c

with A \in\Re^{3 \times 3} is a symmetric Tensor of second order and b,c \in \Re^3 are vectors

Homework Equations

The Attempt at a Solution

(A \times b)_ {ij} = A_{ij} \epsilon _{jkl} b_l

 

[gabbagabbahey]

Let's define another tensor T by T_{ij}=(A \times b)_ {ij} = A_{ij} \epsilon _{jkl} b_l...
what is c \cdot T ?...how about T \cdot c ?