Question

The inverse of a skew symmetric matrix (if it exists) is:

• A. a symmetric matrix
• B. a skew symmetric matrix
• C. a diagonal matrix
• D. none of a matrix is unique

Answer 1

The correct option is B a skew symmetric matrix

As skew symmetric matrix
A be a. skew symmetric matrix
$\therefore A^T=-A$

$A^{-1}=\frac{adjA}{\left|A\right|}$

$(A^{-1}{)}^{T_2}{\left(\frac{adjA}{\left|A\right|}\right)}^T=\frac{adj{A}^T}{\left|A\right|}$

$=\frac{adj-A}{\left|A\right|}$

$=-\frac{adjA}{\left|A\right|}$

$=-A^{-1}$

$\therefore A^{-1}$ is also a skew symmetric.