Find $9^{-1} \pmod{100}$, as a residue modulo 100.  (Give an answer between 0 and 99, inclusive.)
<|im_start|>system
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<|im_start|>user
Find $9^{-1} \pmod{100}$, as a residue modulo 100.  (Give an answer between 0 and 99, inclusive.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
89
Find $9^{-1} \pmod{100}$, as a residue modulo 100.  (Give an answer between 0 and 99, inclusive.)
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