If the matrix is a skew symmetric matrix,

Let $A=\left[\begin{array}{ccc}0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0\end{array}\right]$

As, $A$ is skew - symmetric matrix.

So, we have

$A^{\prime}=-A$

Then,

$\Rightarrow \quad\left[\begin{array}{ccc}0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0\end{array}\right]=-\left[\begin{array}{ccc}0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0\end{array}\right]$

$\Rightarrow \quad\left[\begin{array}{ccc}0 & 2 & c \\ a & b & 1 \\ 3 & -1 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -a & -3 \\ -2 & -b & 1 \\ -c & -1 & 0\end{array}\right]$

By equality of matrices, we get

$a=-2, c=-3$ and $b=-b \Rightarrow b=0$

Hence,

$a=-2, b=0$ and $c=-3$