Consider the following statements:

S1: The sum of two singular n × n matrices may be non-singular S2: The sum of two n × n non-singular matrices may be singular.

Which of the following statements is correct?

A | S1 and S2 are both true |

B | S1 is true, S2 is false |

C | S1 is false, S2 is true |

D | S1 and S2 are both false |