KCET · Maths · Matrices
If \(A\) is a skew symmetric matrix, then \(A^{2021}\) is
- A Row matrix
- B Column matrix
- C Symmetric matrix
- D Skew symmetric matrix
Answer & Solution
Correct Answer
(D) Skew symmetric matrix
Step-by-step Solution
Detailed explanation
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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