Let V be an n-dimensional vector space over a field F. Let B = {e1,..., en} be a fixed but arbitrarily chosen ordered basis of V. Show that
(a) for each linear operator E L(V), there exists a unique matrix A € M₁ (F) such that A = []B and [(u)]B = A[u]s for every u € V;
(b) for each A € M₁ (F), there exists a unique linear operator E L(V) such that [(u)] = A[u]B for every u E V.