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Let A be a matrix which is both symmetric and skew symmetric.

so AT=A and AT= -A

so A =- A

that implies 2A =zero matrix

that implies A is a zero matrix

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Q: Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
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Related questions

Is null square matrix a skew symmetric?

yes, it is both symmetric as well as skew symmetric


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