That depends upon what you mean by "remove". Normally "-" means "subtract". That is defined only for matrices with the same number of rows and columns.
If you mean [itex]a_{ij}- b_{ij}[/itex], taking [itex]b_{ij}= 0[/itex] if i> 2 and j> 3, you can define that (you can define anything) but it will not obey any of the usual algebraic rules- so probably won't be of much use.