Question

The inverse of a skew symmetric matrix of odd order is

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

Answer 1

Answer: (D)

does not exist

Let $A$ be a skew symmetric, matrix of order n.
By definition
$A^{\prime }=-A\Rightarrow |A^{\prime }|=|-A|$
$\Rightarrow |A|=(-1{)}^n|A|\Rightarrow |A|=-|A|$ ($\because$ n is odd)
$\Rightarrow 2|A|=0\Rightarrow |A|=0$
$\therefore A^{-1}$ does not exist.
Hence, option D.