Question

Show that the matrix, $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]$ is a skew -symmetric matrix.

Answer 1

Now, $A^{\prime }={\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]}^{\prime }=\left[\begin{array}{ccc}0& -1& 1\\ 1& 0& -1\\ -1& 1& 0\end{array}\right]=-\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]=-A$
$\therefore A^{\prime }=-A$. Hence, A is skew -symmetric matrix.