`
`
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 ' $b$ '.
Solution:
$A=\left[\begin{array}{ccc}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{array}\right]$
If matrix $\mathrm{A}$ is a skew-symmetric matrix then,
$A^{T}=-A$
$\left[\begin{array}{ccc}0 & 2 & b \\ a & 0 & 1 \\ -3 & -1 & 0\end{array}\right]=-\left[\begin{array}{ccc}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{array}\right]$
$\Rightarrow\left[\begin{array}{ccc}0 & 2 & b \\ a & 0 & 1 \\ -3 & -1 & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -a & 3 \\ -2 & 0 & 1 \\ -b & -1 & 0\end{array}\right]$
$\Rightarrow a=-2$ and $b=3$
.jpg)