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Prove that if matrix A is skew-symmetric, then A.A is symmetric.

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Prove that if matrix A is skew-symmetric, then A.A is symmetric.
Answered Same Day Dec 25, 2021

Solution

Robert answered on Dec 25 2021
130 Votes
A is skew-symmetric <=> A = - AT .
So,

(A.A)T = AT .AT = (- A ).(- A ) = A.A

Hence, A.A is symmetric.
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