If T and S are linear transformations such that T: V -> W and S: U -> V, if TS is bijective does that only happen when T and S are both bijective?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 4CM
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If T and S are linear transformations such that T: V -> W and S: U -> V, if TS is bijective does that only happen when T and S are both bijective?

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So the statement TS is bijective iff T and S are bijective is correct then?

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