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If $A$ is a skew symmetric matrix, then $A^{2021}$ is
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Verified Answer
The correct answer is:
Skew symmetric matrix
Given, $A^T=-A$
Let
$$
\begin{aligned}
P & =A^{2021} \\
P^T & =\left[A^{2021}\right]^T=\left[A^T\right]^{2021} \\
& =[-A]^{2021}=-[A]^{2021}=-P
\end{aligned}
$$
Hence, $A^{2021}$ is also a skew symmetric matrix.
Let
$$
\begin{aligned}
P & =A^{2021} \\
P^T & =\left[A^{2021}\right]^T=\left[A^T\right]^{2021} \\
& =[-A]^{2021}=-[A]^{2021}=-P
\end{aligned}
$$
Hence, $A^{2021}$ is also a skew symmetric matrix.
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