Dr. Frankenine (cousin of Dr. Frankenthree) took positive integers, reversed their digits, and subtracted the two numbers. She noticed all the results were divisible by 9:
\[ \begin{align}
{\color{blue}83}-{\color{green}38} &= 45 \\&= 9 \times 5 \\\\
{\color{blue}113}-{\color{green}311} &= -198 \\&= 9 \times (-22) \\\\
{\color{blue}1431} -{\color{green}1341} &= 90 \\&= 9 \times 10 \\\\
{\color{blue}44344} -{\color{green}44344} &= 0 \\&= 9 \times 0.
\end{align}\]
Are the numbers Dr. Frankenine creates in this way **always** multiples of 9?

**Note:** This puzzle is in base 10.

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