[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] - [A]T, respectively. Which of the following statements is true?
1
Both [S] and [D] are symmetric
2
Both[S] and [D] are skew-symmetric
3
[S] is skew-symmetric and [D] is symmetric
4
[S] is symmetric and [D] is skew-symmetric