Question

what is the multiplicative inverse of -1/9

Answer 1

what number would make -1/9 to be one, if you multiply it (the -1/9) by it.
In other words,

\(\large\color{black}{ -\frac{1}{9} \times (N)=1 }\)

Answer 2

you can logically guess that number,
first it is going to be negative, so that negative times negative will cancel the minus sign.

And then for any 1/a, the multiplicative inverse is a/1
So, in your case "a" is 9, so it would be
9, but not just 9, it is \(\large\color{black}{ -9 }\).