Which of the following matrix is not skew symmetric matrix?

$\left[\begin{array}{cc}0 & -3 \\ 3 & 1\end{array}\right]$

a skew matrix is one which follows following property symmetric 

A = -AT

Transpose of a matrix A

Let A = [a_ij]_m×n

→ A is a matrix of order m×n

a_ij → represents its i^th, j^th element

A^T = [a_ji]_n×m

for skew symmetric matrix

A = -A^T → every a_ij = -a_ji

so for diagonal elements

a_ii = -a_ii → both indices are represented by i, i since its a diagonal element 

⇒ 2a_ii = 0 

⇒ a_ii = 0 → for skew symmetric matrices its diagonal entries are always zero → necessary condition for skew symmetric matrices

So we need to check only these matrices whose diagonal entries are not zero first

In this case we will check

for option 2

$A=\left[\begin{array}{cc}0 & -3 \\ 3 & 1\end{array}\right]$ → non zero diagonal entries

$A^T=\left[\begin{array}{cc}0 & 3 \\ -3 & 1\end{array}\right]$

$-A^T=\left[\begin{array}{cc}0 & -3 \\ 3 & -1\end{array}\right]$

⇒ A ≠ - A^T

option 2 → not skew symmetric matrix