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  4. If A is a skew symmetric matrix such that AT A=I, then A4 n-1(n ∈ N) is equal to -

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

Matrices

Solution:

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