Prove the characteristics of numbers divisible by 11 I want to prove, prove

Prove the characteristics of numbers divisible by 11 I want to prove, prove

Characteristics of numbers divisible by 11
Add a number from the right to the left, and then calculate the difference between the odd and even digits. If the difference is a multiple of 11 (including 0), then the original number must be divisible by 11
Let a1 + 10a2 + 100a3 +. + 10 ^ Nan be a multiplier, multiply by 11 = (10 + 1)=
10a1+100a2+.+10^na(n-1)+10^()n+1 an
+ a1+10a2+100a3+.+10^nan
The difference between the sum of odd and even digits is a multiple of 11