Question

Let A be a skew-symmetric matrix of odd order, then $\left|A\right|$ is equal to

• A. $0$
• B. $1$
• C. $-1$
• D. none of these

Answer 1

The correct option is A $0$

Since, A is skew-symmetric.
$A^{\prime }=-A$
We know that $|kA|=k^n|A|$ where n is order of matrix.
$\therefore |A^{\prime }|=(-1{)}^n|A|$
$\Rightarrow |A|=(-1{)}^n|A|$
$\Rightarrow (1-(-1{)}^n)|A|=O$
If n is odd, then $(1-(-1{)}^n)\ne 0$
$\Rightarrow |A|=0$