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 values of 'a' and 'b'.

Answer 1

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

Since $A$ is skew-symmetric matrix

$\Rightarrow -A=A^t$ ...... $\left(i\right)$

Now, $A^t=\left[\begin{array}{ccc}0& 2& b\\ a& 0& 1\\ -3& -1& 0\end{array}\right]$

From $\left(i\right)$

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

$\Rightarrow a=-2$ and $b=3$