Linear Algebra problem. Please answer all questions. I will give thumb up. Thank you
A, B, P, and D are n x n matrices. Mark each statement True or False. Justify each answer. (Study Theorems 5 and 6 and the examples in Section 5.3 of the textbook for help.) i. A is diagonalizable if A has n eigenvectors ii. If A is diagonalizable, then A has n distinct eigenvalues. iii. If APPD, with D diagonal, then the nonzero columns of P must be eigenvectors of A. iv. If A is invertible, then A is diagonalizable.