electromagnetism - Tensor product notation

In the image there is a tensor product:

$$F_{\mu\nu}F^{\mu\nu}=2(B^2-\frac{E^2}{c^2})$$

It's about how this operation on the co- and contravariant field strength tensors can give one of the invariants of the electromagnetic field.

I've tried it and it's actually the double inner product, F_lower(row,column)*F^upper(column,row) summed over all rows and columns

$$F_{\mu \nu}F^{\nu \mu}$$

Is this the way I would write it with subscript summation?

How did it come?