If A skew-symmetric matrix and n is an o

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

If A skew-symmetric matrix and n is an odd positive integer, then Aⁿ is:

Options:

symmetric matrix

skew-symmetric matrix

diagonal matrix

zero matrix

Correct Answer:

skew-symmetric matrix

Explanation:

A skew-symmetric matrix A, A^T=−A.

$(A^n)^T=(−1)^nA^n$, since n is an odd integer then An is also a skew-symmetric matrix.