If Ais a skew-symmetric matrix and n is odd positive integer, then An is

A
A skew-symmetric matrix
B
A symmetric matrix
C
A diagonal matrix
D
None of these

Solution:

Given Ais skew-symmetric. Hence,
$\begin{array}{l} A^{T} = - A \\ \Rightarrow A^{n} = {(- A^{T})}^{n} = - {(A^{T})}^{n} = - {(A^{n})}^{T} (given n is odd) \end{array}$
Hence, Aⁿ is skew-symmetric

If Ais a skew-symmetric matrix and n is odd positive integer, then Aⁿ is

Solution:

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