Friedel Craft Alkylation Why do we get isoproyl benzene on treating benzene with 1-chloropropane instead of n-propyl benzene?

Is it because of Markovnikov's rule?
First AlCl3 converts 1-chloropropane into propane with a positive charge on terminal carbon

Since secondary carbocation is more stable than primary carbocation it undergoes rearrangement and positive charge shifts to secondary carbonation atom.

Hence we get isopropyl benzene