Even number of 1' s in rows and columns

public class EvenNumberRowsAndColumns {

    public static void main(String[] args) {
        //create matrix and fill with 0 and 1
        int[][] matrix= new int[6][6];
        boolean even = true;
        // fill with randoms 0's and 1's
        for (int i=0; i<matrix.length; i++) {
            for (int j=0; j<matrix[i].length; j++) {
                matrix[i][j] = (int)(Math.random() * 2);
            }
        }
        // check for even rows
        for (int i=0; i<matrix.length; i++) {
            int rowSum=0;
            for (int j=0; j<matrix[i].length; j++) {
                // at this point I need a true or false
                // so I'm going back up and making one
                rowSum+= matrix[i][j];
            }
                if (rowSum % 2 != 0) {
                    even = false;


            }
        }
        // check for even columns
        for (int j=0; j<matrix[0].length; j++) {
            int colSum=0;
            for (int i=0; i<matrix.length; i++) {
                colSum+= matrix[i][j];
            }
            if (colSum % 2 !=0) {
                even = false;

            }
        }
        // print matrix and print result
        for (int i=0; i<matrix.length; i++) {
            for (int j=0; j<matrix[i].length; j++) {
                System.out.print(matrix[i][j]+ " ");

            }
            System.out.println();

    }
        System.out.println(even);

}
}