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## Homework Statement

Let A

_{ijkl}be a rank 4 square tensor with the following symmetries:

[tex]

A_{ijkl} = -A_{jikl}, \qquad A_{ijkl} = - A_{ijlk}, \qquad A_{ijkl} + A_{iklj} + A_{iljk} = 0,

[/tex]

Prove that

[tex]

A_{ijkl} = A_{klij}

[/tex]

## Homework Equations

## The Attempt at a Solution

From the first two properties I concluded that:

[tex]

A_{iikl} = 0 \qquad A_{ijkk} = 0

[/tex]

The last one leaded me to:

[tex]

A_{ikli} = -A_{ilik} \qquad A_{ikkj} = -A_{ikjk}

[/tex]

However I don't see how this last one may help me.