Answer with explanation please A and D are nxn matrices Che

Answer with explanation please

A, ? and D are nxn matrices. Check the true statements below: If A is invertible, then A is diagonalizable. If AP = PD, with D diagonal, then the nonzero columns of ? must be eigenvectors of A. A is diagonalizable if A has n distinct eigenvectors. If A is diagonalizable, then A has n distinct eigenvalues.

Solution

A. False

A needs n distinct eigenvalues for it to be diagonalizable. A being invertible does not guarantee n eigenvalues

B. True

C. True

D. False

It must have n distinct eigenvectors but can have less than n eigenvalues.