I think that without taking any example we can get the answer.

Following is the explaination for the two statements.* statement 1 : *let us consider any two matrices of n-by-n which are singular, where n >= 2 (beacuse for n = 1 we can only have 1 matrix which is singular). Now, the addition of these two matrices may be singular or nonsingular. Assume that all such possible pairs of matrices yield the sum as non-singular, then certainly statement 1 is true. Now, assume only some possible pairs of n-by-n matrices yield the sum as non-singular while others as singular, then also statement 1 is true, due to the keyword

**"**

**may be***in the statement. Now, assume the last possibility that all pairs of such matrices yield as singular matrix , then also statement 1 is true again due to*

**"**

**"**

**may be***keyword. Hence, statement 1 is true for all cases.*

**"*** statement 2 : *we can argue similarly that statement 2 is also true in all cases.

Hence option A is right answer. Please correct me if I am wrong.