If "A" is an nxn matrix show that "A" can be written as the sum of a symmetric matrix and a skew symmetric matrix.

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If "A" is an nxn matrix show that "A" can be written as the sum of a symmetric matrix and a skew symmetric matrix.

Mathematics
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True. Do you need to prove it?
yes
I have a definition in my textbook, and it goes like this.....

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https://in.answers.yahoo.com/question/index?qid=20100824085905AAThbDi
\[A = V+S, where V= \frac{ 1 }{ 2 }(A + A^T), and S = \frac{ 1 }{ 2 }(A - A^T)\]
I know I can use this but I am wondering if there is another way generically that I can show this is true. I am not supposed to use actual numbers in any proofs, so I can't just do these operations to a matrix and show it works out
I will take a look at the link, thank you

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