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There are two things that are confusing me a bit, and was wondering if anyone could explain them.

Firstly, if we let V1,V2,...,Vn be vectors in some field F^n and let P = {V1,V2,....,Vn},

then the following are equivalent:

(i) {V1,V2,....,Vn} is a basis for F^n ;

(ii) P is invertible.

Secondly, let T be a linear map. Then if T is invertible, then it is injective.

Thanks for the hep in advance!

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# Bases, Invertibility and Injectivity Query

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