Question

If $A$ is a $3\times 3$ skew-symmetric matrix, then trace of $A$ is equal to

• A. $1$
• B. $|A|$
• C. $-1$
• D. none of these

Answer 1

The correct option is B $|A|$

As $A$ is a skew symmetric matrix
$A^{\prime }=-A$
$\Rightarrow a_{ii}=0\forall i\Rightarrow trace\left(A\right)=0$
Also $|A|=|A^{\prime }|=|-A|=(-1{)}^3|A|$
$\Rightarrow 2|A|=0\Rightarrow |A|=0$
Hence, option B.