Question

matrix is both symmetric and skew symmetric matrix.

Answer 1

Finding matrix which is both symmetric and skew symmetric.
Since matrix $A$ is symmetric
If $A=A^T$
And matrix $A$ is skew symmetric
if $A=-A^T$
Using eq. (i) and (ii)
$A^T=-A^T$
$\Rightarrow 2A^T=0$
$\Rightarrow A^T=0$
$\Rightarrow A=0$

[Using (i)]
$\therefore A$ is a null matrix.
Hence, null matrix is both symmetric and skew-symmetric matrix.