Question

The inverse of a skew-symmetric matrix of an odd order is

• A. a symmetric matrix
• B. a skew-symmetric matrix
• C. diagonal matrix
• D. does not exists

Answer 1

The correct option is D does not exists

Let $A$ be a skew -symmetric matrix order $n$, by defination $A^{\prime }=-A$

$\Rightarrow |A^{\prime }|=|-A|$

$\Rightarrow |A|=(-1{)}^n|A|$

$\Rightarrow |A|=-|A|...........[\because nisodd]$

$\Rightarrow 2|A|=0$

$\Rightarrow |A|=0$

hence $A^{-1}$ does not exist