Let $A$ be normal $n\times n$ matrix. $c$ is eigen value of A. Than must exist:
if $A+A^*$ invertible then $c=bi$ (b real).
if $A$ invertible then $A+A^*$ invertible.
if $c$ is the only eigenvalue of $A$ and $c=bi$ (b is real) than $A+A^*$ is the zero matrix.
if $A+A^*$ invertible than for every $b$ that is real $c\not=bi$.
all answers 1-4 are false.
The correct answers are 3+4 but I can't understand why