Correct Answer - Option 4 :
[S] is symmetric and [D] is skew-symmetric
Explanation:
Given,
[A] is a square matrix and it is neither symmetric nor skew-symmetric
Also given,
[AT]T = [A]
[S] = [A] + [A]T , [D] = [A] - [A]T
Lets take Case (i)
[S]T = ( [A] + [A]T )T = [A]T + A = [S]
So [S] is a Symmetric Matrix
Now Case (ii)
[D]T = ([A] - [A]T)T = [A]T - [AT]T = [A]T - [A] = - ([A] - [A]T) = - [D]
So [D] is skew Symmetric Matrix