Crossword Genius

Backward maybe, but she’s the woman for many a man (5)

Ross

I believe the answer is:

madam

I'm a little stuck... Click here to teach me more about this clue!

'backward maybe but she's the' is the definition.
I can't judge whether this definition defines the answer.

'woman for many a man' is the wordplay.
'woman' becomes 'ada'.
'for' means one lot of letters go next to another (I've seen this in other clues).
'many' becomes 'm'.
'a man' becomes 'm'.
'ada' after 'm' is 'mada'.
'mada'+'m'='MADAM'

Can you help me to learn more?

(Other definitions for madam that I've seen before include "Courteous form of address to a woman" , "precocious schoolgirl?" , "Woman with status - girl with bad manners" , "Woman of standing" , "Titled lady" .)

I've seen this clue in the Evening Standard.
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