Let $A$ be a $10 \times 10$ matrix with complex entries such that all its eigenvalues are non-negative real numbers, and at least one eigenvalue is positive. Which of the following statements is always false ?
- There exists a matrix $B$ such that $AB-BA = B$.
- There exists a matrix $B$ such that $AB-BA = A$.
- There exists a matrix $B$ such that $AB+BA=A$.
- There exists a matrix $B$ such that $AB+BA=B$.