Explanation: If matrix A is symmetric
AT=A
If matrix A is skew-symmetric
AT=−A
Also, diagonal elements are zero.
Since, it is given that matrix A is both symmetric and skew-symmetric.
∴‌‌A=AT=−A
Which is only possible if A is zero matrix.
A=[

0	0
0	0

]=AT=−A
Thus, if a matrix A is both symmetric and skew symmetric, then A is necessarily a zero matrix.