Question

If the matrix $A=\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right]$ is skew-symmetric, find the value of 'a' and 'b'.

Answer 1

$A=\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right]$
If matrix A is a skew-symmetric matrix then,
$A^T=-A$
$$\begin{gathered} \left[\begin{array}{ccc}0& 2& b\\ a& 0& 1\\ -3& -1& 0\end{array}\right]=-\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right] \\ \Rightarrow \left[\begin{array}{ccc}0& 2& b\\ a& 0& 1\\ -3& -1& 0\end{array}\right]=\left[\begin{array}{ccc}0& -a& 3\\ -2& 0& 1\\ -b& -1& 0\end{array}\right] \\ \Rightarrow a=-2\mathrm{and}b=3 \end{gathered}$$