Search in a sorted 2D matrix

import java.util.*;

public class tUf {
    public static boolean searchMatrix(ArrayList<ArrayList<Integer>> matrix, int target) {
        int n = matrix.size(), m = matrix.get(0).size();

        // traverse the matrix:
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (matrix.get(i).get(j) == target)
                    return true;
            }
        }
        return false;
    }


    public static void main(String[] args) {
        ArrayList<ArrayList<Integer>> matrix = new ArrayList<>();
        matrix.add(new ArrayList<>(Arrays.asList(1, 2, 3, 4)));
        matrix.add(new ArrayList<>(Arrays.asList(5, 6, 7, 8)));
        matrix.add(new ArrayList<>(Arrays.asList(9, 10, 11, 12)));

        boolean result = searchMatrix(matrix, 8);
        System.out.println(result ? "true" : "false");
    }
}