Yes, it is a good thinking .. If anyone has read Herbert Schildt or Deitel's Java books would have recognized it.. my solution is the same.. some one else should be able to read it quickly..

static int diagonalDifference(int[][] a) {
    int primeDi = 0, secondDi = 0;
    // could be improved to 
            // int sum = 0;
    for (int i = 0 , j = a[0].length-1; i < a[0].length ; i++, j--) {
        primeDi += a[i][i] ;
        secondDi += a[i][j] ;
                    // could be improved to 
                    // sum = a[i][i] - a[i][j] ;
    }

    return Math.abs(primeDi - secondDi);
            // could be improved to
            // return Math.abs(sum);
}