10. True or False

(a) (3%) If $A$ is an $n \times n$ matrix whose eigenvalues are all nonzero, then $A$ is nonsingular.

(b) (3%) If $A$ is a $5 \times 5$ matrix of rank 1 and $\lambda = 0$ is an eigenvalue of multiplicity 4, then $A$ is diagonalizable.