K^n/Multiplication in coordinate system/Not compatible/Exercise

Let ${}v_{1},\ldots ,v_{n}$ be a basis of ${}K^{n}$, and let

$\psi _{\mathfrak {v}}\colon K^{n}\longrightarrow K^{n},{\begin{pmatrix}s_{1}\\\vdots \\s_{n}\end{pmatrix}}\longmapsto s_{1}v_{1}+s_{2}v_{2}+\cdots +s_{n}v_{n},$

be the corresponding bijective mapping in the sense of remark. Show that this mapping is, in general, not compatible with componentwise multiplication in ${}K^{n}$.

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