They really are 2 very similar things, zero and nine.
Their similar behaviors are shown best through adding and multiplying.

0 + 1 = 1
9 + 1 = 10 = 1 (1+0=1)

0 + 2 = 2
9 + 2 =11 = 2 (1+1=2)

0 + 3 = 3
9 + 3 = 12 = 3 (1+2=3)
Etc..

Its only when subtracting, and dividing, do they behave somewhat differently.
Otherwise when adding and multiplying, they act pretty much the same exact way.

0 x 1 = 0
9 x 1 = 9

0 x 2 = 0
9 x 2 = 18 = 9 (1+8=9)

0 x 3 = 0
9 x 3 = 27 = 9 (2+7=9)
Etc..