The multiplicative inverse would be the fraction 1/9 which is 1 over 9.
In short, we think of 9 as 9/1 and then take the reciprocal
Multiplying 9 and 1/9 leads to 1
9*(1/9) = (9/1)*(1/9) = (9*1)/(1*9) = 9/9 = 1