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Let $A^{\#}:A_{n}(F)\rightarrow A_{n}(E)$ define by $A^{\#}f(v_{1},\cdots ,v_{n})=f(Av_{1},\cdots, Av_{n})$, where $A_{n}(F)$ is the space of the alternated n multilinear forms in F. Verify that $(\alpha A)^{\#}=\alpha (A^{\#})$, where $\alpha$ is a scalar and $A:E\rightarrow F $ is a linear transformation.

$(\alpha A)^{\#}f(v_{1},\cdots ,v_{n})=f(\alpha Av_{1},\cdots,\alpha Av_{n})=\alpha^{n}f(Av_{1},\cdots, Av_{n})\neq \alpha (A^{\#})f(v_{1},\cdots ,v_{n})$

then I showed that it's false, am I missinterpreting all?

a hint would be appreciated, thanks in advance .

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    @missing unfortunately I don't know Portuguese `:-(`2011-07-01

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