If matrix $\left[ {\begin{array}{cccccccccccccccccccc}0&a&3\\2&b&{ - 1}\\c&1&0\end{array}} \right]$ is a skew-symmetric matrix, then find the values of $a,b$ and $c$.

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

Since, $A$ is skew-symmetric matrix.

$\therefore$ ${A^\prime } = - A$

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

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

By equality of matrices,

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

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