If we look at its mirror image about a mirror which is perpendicular to plane of the molecule, the two $\ce{-CH3}$ groups which are pointing upwards and downwards (implied by the wedge and the dash) will interchange their positions:

[!["mirror plane" or trans-1,2-dimethylcyclobutane][1]][1]

But also the mirror image would be perfectly superimposable on 1,2-dimethylcyclobutane. Hence, it should be achiral, but the answer key says it is chiral. Is this compound an exception?


  [1]: https://i.sstatic.net/U3OCc.png