Let V be a vector space with addition of vectors denoted by '+' multiplication of vectors by scalars denoted by *.*. For example, 2 v + 3 w is 2 times the vector v plus 3 times me vector w. Let t : V -> V be a bijection. Define two new operations "+f" and "f" as follows. If v and w are two vectors in V. v +f w is defined to be the vector f* (-1)(f(v) + f(w)) where f*(-1) is the inverse function of f. If a is a scalar and v is a vector in V, a f v is defined to be the vector f*(-1)(a f(v)) Prove that V together with the new addition of vectors, +f, and the new multiplication of vectors by scalars, f, is also vector space.
