What's So Special About Eleven?

\[\large 88, \ \ \ 1441, \ \ \ 3553, \ \ \ 269962 , \ \ \ 1357997531 \]

The above are some examples of palindromes with an even number of digits, and they so happen to be all divisible by 11. Is it true that all palindromes with an even number of digits are all divisible by 11?

Assume all palindromes are whole numbers.

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