Reversal Nines

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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