pproving (g ° f)* = f* ° g* -- is this correct? 1. The problem statement, all variables and given/known data 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?