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 $T \cdot c$ ?