You have a pretty crucial bug in your program. You will never reach the end of the maze!
if(x == maze.mazeMatrix.length && y == maze.mazeMatrix.length)
references indices that are out of bounds! It should be
if(x == maze.mazeMatrix.length - 1 && y == maze.mazeMatrix.length - 1)
You also need to check to see whether you can & should move before you try to move there. I.E. :
while (!mazeCompleted){
boolean moveRight = (x + 1 < mazeMatrix.length && maze.mazeMatrix[x+1][y] == 0 ? true : false);
boolean moveLeft = (x - 1 >= 0 && maze.mazeMatrix[x-1][y] == 0 ? true : false);
boolean moveUp = (y + 1 < mazeMatrix[x].length && maze.mazeMatrix[x][y+1] == 0 ? true : false);
boolean moveDown = (y - 1 >= 0 && maze.mazeMatrix[x][y-1] == 0 ? true : false);
And:
else if(moveRight) { // Move right.
maze.mazeMatrix[x+1][y] = 2;
x++; nSteps++;
}
etc. Although it does seem like this is something that should be solved recursively, as if there are any loops in the maze you will end up getting stuck and infinite looping.