A) a skew-symmetric matrix
B) a symmetric matrix
C) a diagonal matrix
D) None of the above
Correct Answer: A
Solution :
Given A is skew-symmetric matrix. \[\therefore \] \[{{A}^{T}}=-A\] \[\Rightarrow \] \[{{A}^{n}}={{(-{{A}^{T}})}^{n}}=-{{({{A}^{T}})}^{n}}={{(-{{A}^{n}})}^{T}}\] Hence,\[{{A}^{n}}\]is skew-symmetric matrix.You need to login to perform this action.
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