Divergence of Energy-momentum Tensor

[ClaraOxford]

How do you prove that Maxwell's energy-momentum equation is divergence-free?
I don't know whether or not I have to use Lagrangians or Eistein's tensor, or if there's a simlpler way of expanding out the tensor..

∂[itex]_{\mu}[/itex]T[itex]^{\mu\nu}[/itex]=0

T[itex]^{}\mu\nu[/itex]=F[itex]^{}\mu\alpha[/itex]F[itex]^{}\nu[/itex][itex]_{}\alpha[/itex]-1/4F[itex]^{}\alpha\beta[/itex]F[itex]_{}\alpha\beta[/itex][itex]\eta[/itex][itex]^{}\mu\nu[/itex]

 

[ClaraOxford]

I mean

∂[itex]_{\mu}[/itex]T[itex]^{\mu\nu}[/itex]=0

T[itex]^{\mu\nu}[/itex]=F[itex]^{\mu\alpha}[/itex]F[itex]^{\nu}[/itex][itex]_{\alpha}[/itex]-1/4F[itex]^{\alpha\beta}[/itex]F[itex]_{\alpha\beta}[/itex][itex]\eta[/itex][itex]^{\mu\nu}[/itex]

 

[vela]

Try writing [itex]F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu[/itex] and using the commutativity of the derivatives.