what is unique inverse?

Asked by  | 9th May, 2008, 08:36: PM

Expert Answer:

f: X to Y is invertible.

this means, f has an inverse

let g: Y to X be inverse of f = f  -1

g o f = f o g = I

let inverse is not unique. let   g1 : Y to X be another inverse of f

g1 o f =f o g1 = I

g1 o f =g o f

composing both sides with g, we get

(g1 o f) o g = (g o f) o g

g1 o (f o g) = g o (f o g)

g1 o I = g o I

g1 = g

hence, inverse is unique.

Answered by  | 16th Jul, 2008, 09:47: AM

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