Question

If the matrix $A=\left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right]$ is skew-symmetric, then:

• A. $a=-2$
• B. $a=2$
• C. $b=3$
• D. $b=-3$

Answer 1

Answer: (A), (C)

$b=3$

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

We know that $A$ matrix is skew-symmetric if $A=-A^T$
$\therefore \left[\begin{array}{ccc}0& a& -3\\ 2& 0& -1\\ b& 1& 0\end{array}\right]=-\left[\begin{array}{ccc}0& 2& b\\ a& 0& 1\\ -3& -1& 0\end{array}\right]$

We know that if matrices are equal then their corresponding elements are equal.
$\Rightarrow a=-2\text{and}b=3$