I tried with induction, but it doesn't works.
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For $2\times 2$ matrices it works. – logarithm May 13 '19 at 21:18
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No, matrices n x n. – Jordan Hernandez May 13 '19 at 21:19
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Note that $f(rA)=r^nf(A)$. This is, $f$ is homogeneous of degree $n$. Quadratic forms are homogeneous of degree $2$. – logarithm May 13 '19 at 21:20
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What are the variables? – herb steinberg May 13 '19 at 21:20
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Now, there is a image with the question.I do not know if it's well raised – Jordan Hernandez May 13 '19 at 21:24
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Where it says $n$ it should say $2$. The matrix $S$ will have a $1/2$ at positions $(1,2)$ and $(2,1)$ and a $-1/2$ at positions $(3,4)$ and $(4,3)$. – logarithm May 13 '19 at 21:27