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Exercise 2.4.9

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If $AB$ is invertible then $L_{AB}$ is invertible. So $L_{A} L_{B} = L_{AB}$ is surjective and injective. And thus $L_{A}$ is surjective and $L_{B}$ injective by Exercise 2.3.12. But since their domain and codomain has the same dimension, actually they are both invertible, so are $A$ and $B$ .

jephianlin

2011-06-27 00:00

Exercise 2.4.9

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