If A is a square matrix, then which among the following is/are true ?

(i) $$A + A'$$​ is a symmetric matrix.
(ii) $$A − A'$$​ is a symmetric matrix.
(iii) $$AA'$$​ is a skew symmetric matrix.

Correct option is A

Given:
A is a square matrix and A' denotes the transpose of A.
Formula used:
​$$(A + A')' = A' + A\\(A − A')' = A' − A\\(AB)' = B'A'$$​​
Solution:
(i) (A + A')' = A' + A = A + A'
So, A + A' is symmetric.
(ii) (A − A')' = A' − A = −(A − A')
So, A − A' is skew symmetric, not symmetric.
(iii) (AA')' = (A')' A' = AA'
So, AA' is symmetric, not skew symmetric.
The correct answer is (a) only (i) is true.