Digit sums of multiples of 11

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Some multiples of 11 have an even digit sum.
For example-
7*11 = 77 and 7+7 = 14, which is even;
11*11 = 121 and 1+2+1 = 4, which is even.

Do all multiples of 11 have an even digit sum?
(Prove that they do or find the smallest that does not.)

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    Best answer

    using 11 division test we know abcdef if divisible by 11
    a + c+e+(b+d+f)=2(sum of even or odd places) + some multiple of  11 having less digits then abcdef.now suppose statement in question works till n digits where n is any number then it will work for n+1 digits we just prove it works when n =2  so i did it

    Yodha Expert Answered on 4th April 2016.
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