Let T be a linear operator on a finite-dimensional vector space V, and let β be an ordered basis for V, we define det(T) = det ( [T]β )

i) 1) Prove that det(T – tIv) = det ( [T]β – tI ) for any scalar t and any ordered basis β

ii) 2) Prove that if det (T) ≠ 0 , then T is invertible