Show for tensors (A · B) : C = A^T · C : B = C · B^T : A

[bubbles_kav]

Homework Statement

using Einstein notation, show the following identities are true

(A · B) : C = A^T · C : B = C · B^T : A

Homework Equations

The Attempt at a Solution

(A · B) : C=(A_{ij} · B_{jk} ) : C
= D_{ik} C_{ik}
= C_{ik} D_{ik}
= C_{ik} (A_{ij} · B_{jk} )

That's as far as I can get. No clue as what to do next, any pointers would be
greatly appreciated :)

 

[clamtrox]

B_jk = B^T_kj

 

[bubbles_kav]

Thanks for the response :)
I got it solved since then, I had trouble trying to convert the double inner product as
a summation. Once I figured that out, it was as easy as pie