If $A$ is a skew-symmetric matrix and $n$ is odd positive integer, then $A^{n}$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Given A is skew-symmetric Hence,
$A^{T} = - A$
$\Rightarrow A^{n} = \left( - A^{T} \right)^{n} = - \left( A^{n} \right)^{T}$ (given $n$ is odd)
Hence, $A^{n}$ is skew-symmetric

Q. If $A$ is a skew-symmetric matrix and $n$ is odd positive integer, then $A^{n}$ is

Explanation

Reviewed by Dr. Abubacker

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