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Out of the following a skew-symmetric matrix is
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$\left[\begin{array}{ccc}0 & 4 & 5 \\ -4 & 0 & -6 \\ -5 & 6 & 0\end{array}\right]$
In a skew-symmetrix matrix $a_{i j}=-a_{j i}$ where $i, j=1,2,3$
for $j=i, a_{i i}=-a_{j i} \Rightarrow$ each $a_{i i}=0$.Hence the matrix $\left[\begin{array}{ccc}0 & 4 & 5 \\ -4 & 0 & -6 \\ -5 & 6 & 0\end{array}\right]$ is skew-symmetric.
for $j=i, a_{i i}=-a_{j i} \Rightarrow$ each $a_{i i}=0$.Hence the matrix $\left[\begin{array}{ccc}0 & 4 & 5 \\ -4 & 0 & -6 \\ -5 & 6 & 0\end{array}\right]$ is skew-symmetric.
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