Let A be a 3 × 3 matrix with real entries. Which of the following assertions is FALSE?
1
A must have a real eigenvalue.
2
If the determinant of A is 0 , then 0 is an eigenvalue of A.
3
If the determinant of A is negative and 3 is an eigenvalue of A, then A must have three real eigenvalues.
4
If the determinant of A is positive and 3 is an eigenvalue of A, then A must have three real eigenvalues.