You talk about a multidimensional matrix but obviously mean a two dimensional matrix - right?
You talk about a matrix of size: N x N but neither the given code signaure nor the task description specify where the value N is given. In your examples you create the matrix by continuous incrementing the root node of matrix - the root node is equal to N, is this always valid or just in your examples or in other words, would this be a valid call:

kill box
set box(1)="A,B"
set box(2)="C,D"

do ##class(codeGolf.ClockwiseWord).Solution(.box,1,1)

I know, I one can obtain the value for N with a simple $order()

set N = $order(matrix(""),-1)

You expect a correct solution, we expect correct a description
justmy2cents
 

Before you start reading, set the lineterminator property to the desired value

 do myStream.Rewind()
 set myStream.LineTerminator=$c(13,10)  // or $c(10)
 
 // or more general
 set myStream.LineTerminator=$case($zversion(1), 2:$c(13,10), 3:$c(10), :"")
 
 // now start reading
 set line = myStream.ReadLine()
 ...
 ...

And do not forget, if the application has/uses parts of "older code" then the so called "naked syntax" may also be a issue (of course not, if you just want to know the name of the global).

Classmethod Test()
{
  kill ^myGlobal
  kill ^yourGlobal
  set ^myGlobal(2)="some data"
  do ..moreData("data1")
  set ^yourGlobal(3)="other data"
  do ..moreData("data2")
  
  // Now, the globals look like
  //
  // ^myGlobal(2)="some data"
  // ^myGlobal(9)="data1"
  //
  // ^yourGlobal(3)="other data"
  // ^yourGlobal(9)="data2"
}

ClassMethod moreData(data)
{
  set ^(9)=data	
}

Beside all the "nice" combinations of direct sets, indirections, naked synates etc. do not forget, your application may call routinies/methods which are in deployed mode (third party APIs and utilities - hopefully with  documentation)