If A be a n × n real matrix. Then, which of the following statements is satisfied conditions for the matrix?
1
If rank (A) = r, then A has r non-zero eigenvalues.
2
If A ^ k = 0 for some k > 0, then trace (A) = 0
3
If the eigenvalues of A are λ1,...,λn, then A is similar to a diagonal matrix with λ1,...,λn along the diagonal
4
If A has a repeated eigenvalue, then A is not diagonalizable