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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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Related answers

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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A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At

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If your graph is undirected, then its adjacency matrix will be symmetric.

Faizan

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Symmetric Matrix:

Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.

note: No need to think about diagonal elements, they can be anything.

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The eigen values of a real symmetric matrix are all real.

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