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Exercise 4

Avg difficulty 2.5

Explain why the following statements are true.

  1. If BB is invertible, then Nul(BA)=Nul(A)\nul(BA) = \nul(A).

  2. If BB is invertible, then Col(AB)=Col(A)\col(AB) = \col(A).

  3. If A∼A′A\sim A', then Nul(A)=Nul(A′)\nul(A) = \nul(A').

Austin, Understanding Linear Algebra, §3.5 Subspaces, Exercise 4

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.