A) A symmetric matrix
B) Skew-symmetric matrix
C) Diagonal matrix
D) None of these
Correct Answer: D
Solution :
Since A is a skew-symmetric matrix, therefore \[{{A}^{T}}=-A\Rightarrow {{({{A}^{T}})}^{n}}={{(-A)}^{n}}\]\[\Rightarrow \]\[{{({{A}^{n}})}^{T}}=\left\{ \begin{align} & {{A}^{n}}\text{, if }n\,\text{is even} \\ & -{{A}^{n}}\text{, if }n\text{ is odd} \\ \end{align} \right.\]
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