Is 8/9 the multiplicative inverse of -1(1/8)? Why or why not?

Since multiplicative inverse of a rational number a is (1/a), if ax1/a=1.
Therefore, 8/9x(-9/8)=8/9x-9/8=-1
But its product must be positive 1.
Therefore, 8/9 is not the multiplicative inverse of (-9/8)

Class 8 Maths Chapter 1 Exercise 1.1 Solution in Video

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https://www.tiwariacademy.com/ncert-solutions/class-8/maths/chapter-1/