[LeetCode]Set Matrix Zeroes

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place.

Follow up:

Did you use extra space?

A straight forward solution using O(mn) space is probably a bad idea.
A simple improvement uses O(m + n) space, but still not the best solution.
Could you devise a constant space solution?

public class Solution {
	public void setZeroes(int[][] matrix) {
		int row = matrix.length;
		int column = matrix[0].length;
		int[][] clone = new int[row][column];
		for (int i = 0; i < row; i++) {
			for (int j = 0; j < column; j++) {
				clone[i][j] = matrix[i][j];
			}
		}
		for (int i = 0; i < row; i++) {
			for (int j = 0; j < column; j++) {
				if (clone[i][j] == 0) {
					for (int k = 0; k < row; k++)
						matrix[k][j] = 0;
					for (int k = 0; k < column; k++)
						matrix[i][k] = 0;
				}
			}
		}
	}
}