Question: Let V be a finite dimensional vector space and consider S,T in End(V). 1. Show that ST is invertible if and only if both S

Let V be a finite dimensional vector space and consider S,T in End(V).

1. Show that ST is invertible if and only if both S and T are invertible.

2. Prove that ST=I iff TS=I

3. Give an example illustrating that both 1 & 2 are false over an infinite dimensional vector space.

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