One thing I noticed is that for any integer $-10<a<10$, $11a$ is always a palindrome. I'm assuming this is because 11 is the first row of Pascal's triangle. For that same reason, for any nonnegative integer $n<5$, $(11a)^n$ is a palindrome.
Is there a proof for this? Is there a proper formula that proves that multiples of 11 are palindromes?