Let $A$ and $B$ be two square matrices that have full rank. Let $\lambda_{A}$ be an eignevalue of $A$ and $\lambda_{B}$ an eigenvalue of $B$. Which of the following is always $\text{TRUE}?$
- $A B$ has full rank
- $A-B$ has full rank
- $\lambda_{A} \lambda_{B}$ is an eigenvalue of $A B$
- $A+B$ has full rank
- At least one of $\lambda_{A}$ or $\lambda_{B}$ is an eigenvalue of $A B$