##### 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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