Let V be an inner product space over F, let T: V → V be a projection. We say that T is an orthogonal projection whenever im(T) = ker(T). (a) Prove that if T = L(V) is an orthogonal projection then ker(T)¹ = im(T). (b) Prove that if P = L(V) is such that P² = P and ||P(v)|| ≤ ||v|| for all v € V, then P is an orthogonal projection.