Direction of the Maxwell stress tensor

[aftershock]

Homework Statement

Show that in vacuum the pressure tensor of a (complex) plane electromagnetic wave only has a contribution for both directions in this bivector being
along the direction of motion, and that contribution is equal in magnitude to
the energy density. HINT: Choose 3 orthogonal axes along the direction of
motion, the electric vector, and the magnetic vector.

Homework Equations

σ_ij = ε₀(E_iE_j -0.5$\delta$_ijE²) + [itex]\frac{1}{μ₀}[/itex] (B_iB_j-0.5$\delta$_ijB²)

The Attempt at a Solution

I'm not entirely sure what this question is asking. Is it saying that the tensor only acts along the direction of motion of the EM wave?

If so the only place I can think to begin is that when i=j the delta term is simply 1 and when they're not equal the term is 0. I'm not sure I can even use that without first showing why that happens though.

 

[BigJDubs]

I know that the energy density of an EM wave is given by \frac{1}{2}\varepsilon_0E^2+\frac{1}{2}\mu_0B^2 and if I let the 3 axes be along the direction of motion, the electric vector and the magnetic vector then the term \deltaijE2 would equal 1 for i=j and 0 otherwise. Does that help to prove what this question is asking?