Exercise4

Explain why the following statements are true.

  1. If \(B\) is invertible, then \(\nul(BA) = \nul(A)\text{.}\)

  2. If \(B\) is invertible, then \(\col(AB) = \col(A)\text{.}\)

  3. If \(A\sim A'\text{,}\) then \(\nul(A) = \nul(A')\text{.}\)

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