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**pproving (g ° f)* = f* ° g* -- is this correct?**

## Homework Statement

assume g: F→G is a linear map

prove that (g ° f)* = f* ° g*

**My solution**

(g ° f)* = g* ° f* by the properties of associativity in linear maps.

if we assume that g* ° f* = f* ° g* then g and f are inverse functions of each other.

by the properties of linear maps the only way that g* ° f* = f* ° g* is if they are inverse functions.

therefore (g ° f)* = f* ° g*

is there anything wildly wrong with my reasoning?