The compound shown is decalin (bicyclo[4.4.0]decane) drawn with the two bridgehead hydrogens on opposite faces (trans-fused). Considering configuration only, which statement is correct?

In trans-decalin the bridgehead hydrogens point to opposite faces and the molecule possesses a centre of symmetry at the midpoint of the shared bond, so it is achiral. In cis-decalin the bridgehead hydrogens are on the same face; a mirror plane perpendicular to the shared bond exchanges the two identical six-membered rings, so cis-decalin is also achiral by configuration (its two chair-chair conformers are enantiomeric but interconvert rapidly). Decalin therefore has only 2 configurational stereoisomers, cis and trans, both optically inactive.