The Beauty of 9

Yesterday was our granddaughter's birthday.  I was telling her what a special birthday it is because her birthday was on 9-9-18 (1+8=9).

Mathematics is so amazing!!  Did you know that multiplying by 9 perpetuates 9s?

1x9=9              9+0=9
2x9=18            1+8=9
3x9=27            2+7=9
4x9=36           3+6=9
5x9=45           4+5+9
6x9=54            5+5=9
7x9=63            6+3=9
8x9=72            7+2=9
9x9=81             8+1=9
10x9=90          9+0=9
11x9=99    9+9=18=1+8=9
12x9=108
13x9=117
14x9=126    1+2+6=9
.
.
21x9=189 1+8+9=18=1+9+9
.
.
32x9=288  2+8+8=18=1+8=9
.
Let's take a random number like 116.
116x9=1044   1+0+4+4=9
.
.
1167x9 = 10503     1+0+5+0+3+9

How about a really random number?
438675x9=  3948075  3+9+4+8+0+7+5=36  3+6=9

I think this is absolutely amazing!!  I wish I understood why.  Any comments?