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Any math geeks here?

Does anyone know why regardless of what integer number you multiply by 9, the sum of the digits of the result is always 9?
149=126 1+2+6=9
529=468 4+6=10 1+0=1 1+8=9
879=783 7+8=15 1+5=6 6+3=9
563249=506916 5+6=11 1+1=2 2+9=11 1+1=2 2+1+6=9

1 x 9 = 09 > 0 + 9
2 x 9 = 18 > 1 + 8
3 x 9 = 27 > 2 + 7
4 x 9 = 36 > 3 + 6
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with each multiplication, the right digit decreases by 1 and the left digit increase by 1 so the sum of the digits will always remains the same, 9. A similar pattern may also apply to higher digit numbers. I'am not a math geek and this may not be the correct reason, but thinking about it, I just got this pattern.