pls explain the answer a little bit, thank you Let A Mm,n(F) and let...

pls explain the answer a little bit, thank you. Let A âˆˆ Mm,n(F) and let TA...

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pls explain the answer a little bit, thank you.
Let A âˆˆ Mm,n(F) and let TA : F n â†’ F m be the correspondinglinear map (see (1.2)). (a) Prove that A has a left inverse if andonly if TA is injective. (b) Prove that A has a right inverse ifand only if TA is surjective. (c) Prove that A has a two-sidedinverse if and only if TA is an isomorphism.

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IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE THERETO HELP YOU ALL THE BESTAnswerExplanationa Suppose that has a left inverse thenis the identity matrix If such that thenThus isinjectiveConversely suppose that is injective Thenthe map is a linear isomorphism Let be See Answer

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