Suppose f: A --> A and g: A --> A are both bijections. Prove or disprove: the composition of g and f is a bijections from A to itself. Solution Consider g(f(x1))=g(f(x2)) Since g is bijection f(x1)=f(x2) Since f is bijection x1 = x2 So gof is one one. And g(f(x)) =y for every y there exists a f(x) = y\' since g is bijective and for every y\' there exists x since f is bijective therefore for every y there exists x such that gof(x)=y gof is on to =>gof is bijective..