i need to prove the next statement:(adsbygoogle = window.adsbygoogle || []).push({});

let S and T be linear operators on a vector space V, then det(SoT)=det(S)det(T).

my way is this:

let v belong to V, and {e_i} be a basis of V

v=e1u1+...+e_nu_n

then T(v)=e1T(u1)+...+enT(un)

(SoT)(v)=S(T(v))=S(e1T(u1)+...+enT(un))=e1S(T(u1))+...+enS(T(un))

but i don't know how to proceed from here.

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# Homework Help: Linear operators question

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