計算機數學

(4分) How many of the following statements are False?

(1) If $A$ is invertible and 1 is an eigenvalue of $A$, then 1 is also an eigenvalue of $A^{-1}$. (2) If $A$ contains a row or column of zeros, then 0 is a eigenvalue of $A$. (3) Each eigenvector of $A$ is also an eigenvector of $A^2$. (4) Each eigenvalue of $A$ is also an eigenvalue of $A^2$. (5) Eigenvectors must be nonzero vectors.