Consider the following statements:
- S1: The sum of two singular $n \times n$ matrices may be non-singular
- S2: The sum of two $n \times n$ non-singular matrices may be singular
Which one of the following statements is correct?
- $S1$ and $S2$ both are true
- $S1$ is true, $S2$ is false
- $S1$ is false, $S2$ is true
- $S1$ and $S2$ both are false