Q. The inverse of a skew-symmetric matrix of odd order is
A) A symmetric matrix
B) A skew symmetric
C) Diagonal matrix
D) Does not exist
Explanation
(d)
Let A be a skew-symmetric matrix of order $n$. By definition,
$A^{'} = - A$
$\Rightarrow \ \ |A'| = | - A|$
$\Rightarrow \ |A| = ( - 1)^{n}|A|$
$\Rightarrow \ |A| = - |A|\lbrack\because n\ is\ odd\rbrack$
$\Rightarrow 2|A| = 0$
$\Rightarrow \ \ |A| = 0$
Hence, $A^{- 1}$ does not exist
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.