Question

$A$ skew-symmetric matrix $A$ satisfies the relation $A^2+I=0$, where $I$ is a unit matrix then $A$ is

• A. idempotent
• B. orthogonal
• C. of even order
• D. odd order

Answer 1

Answer: (B), (C)

The correct options are
B orthogonal
C of even order

Given: $A^2+I=0$

$\Rightarrow A^2=-I$

Property of orthogonal matrix $A^2=I$ if $A$ is of odd order and

$A^2=-I$ if $A$ is of even order.

Hence, $A$ is an orthogonal matrix of even order.