##### Exercise7

Provide a justification for your response to the following questions.

1. Suppose that $$A$$ is a square matrix with two identical columns. Can $$A$$ be invertible?

2. Suppose that $$A$$ is a square matrix with two identical rows. Can $$A$$ be invertible?

3. Suppose that $$A$$ is an invertible matrix and that $$AB = AC\text{.}$$ Can you conclude that $$B = C\text{?}$$

4. Suppose that $$A$$ is an invertible $$n\times n$$ matrix. What can you say about the span of the columns of $$A^{-1}\text{?}$$

5. Suppose that $$A$$ is an invertible matrix and that $$B$$ is row equivalent to $$A\text{.}$$ Can you guarantee that $$B$$ is invertible?

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