Please help with the explanation (Statement True/False)

Thanks

. For every A G M3 UK), there exists an eigenvector of A (hint: the answer is not the same if we change the size of the matrix from 3 to 2); . Eigenvalues must be nonzero; . Suppose A 6 M2 (F) has two distinct eigenvalues. The set of all eigenvectors of A is a subspace of R2; . The eigenvalues of an upper triangular matrix A are the diagonal entries of A