Q85 / 180 · KCET 2022 · Mathematics
If $A$ is a skew symmetric matrix, then $A^{2021}$ is
- ARow matrix
- BColumn matrix
- CSymmetric matrix
- Correct answerDSkew symmetric matrix
Solution
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.
Hence, the correct answer is option: 'D'.