Question

For what value of $x$, is the matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 3\\ x& -3& 0\end{array}\right]$ a skew symmetric matrix?

Answer 1

Given: $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 3\\ x& -3& 0\end{array}\right]$ is a skew matrix.

We know that any square matrix $A=\left[a_{ji}\right]$ is said to be skew symmetric if $A^{\prime }=-A$, that is $\left[a_{ij}\right]=-\left[a_{ji}\right]$ for all possible value of $i$ and $j.$

$A^{\prime }=\left[\begin{array}{ccc}0& -1& x\\ 1& 0& -3\\ -1& 3& 0\end{array}\right]$ $=-A=\left[\begin{array}{ccc}0& -1& 1\\ 1& 0& -3\\ -x& 3& 0\end{array}\right]$

On comparing, we get $x=1$

Therefore, the value of $x$ will be $1.$