Let V be an n-dimensional vector space with basis B = {v1 , . . . , vn}. Let P be an invertible n X n matrix and set
ui = p1iv1 + ∙ ∙ ∙ + pni vN
for i = 1 , . . . , n. Prove that C = {u1 , . . . , un} is a basis for V and show that P = PB←C·