Question

If $A$ 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

Answer: (D)

$A^T=-A.\&A^{T}A=I$
$\Rightarrow A^2=-I\Rightarrow A^{4n}=I$
$A^{4n-1}=A^{-1}\Rightarrow A^{4n-1}=A^T$ (A is orthogonal)