Question

A is a skew symmetric matrix such that $A^{T}A=I$, then $A^{4n-1}(n\in N)$ is equal to

• A. $-A^T$
• B. $I$
• C. $-I$
• D. $A^T$

Answer 1

The correct option is D $A^T$

$A^T=-A$ & $A^{T}A=I$
$\Rightarrow A^2=-I\Rightarrow A^{4n}=I$
$\therefore A^{4n-1}=A^{-1}=A^T$