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If AA is a skew-symmetric matrix and nn is an odd positive integer, then AnA^n is :

Solution

✅ Correct Option: 2

If AT=−AA^T = -A, then (An)T=(AT)n=(−A)n=(−1)nAn=−An(A^n)^T = (A^T)^n = (-A)^n = (-1)^n A^n = -A^n for odd nn. So AnA^n is skew-symmetric.

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