# Does a Turing Machine with a 2-dimensional tape recognize RE languages? [duplicate]

This question is from a Computer Theory Course

What is the category of languages recognized by a MT with a two-dimensional tape? The Tape is an infinite matrix. For each move the head shift belongs to the set $S$ = {stop, north, east, south, west}

My approach

I know that TM recognize Recursively Enumerable or type $0$ languages, but how to show a proof for this answer?