##### Exercise3

Determine whether the following statements are true or false and provide a justification for your response.

1. If $$A$$ is invertible, then $$A$$ is diagonalizable.

2. If $$A$$ and $$B$$ are similar and $$A$$ is invertible, then $$B$$ is also invertible.

3. If $$A$$ is a diagonalizable $$n\times n$$ matrix, then there is a basis of $$\real^n$$ consisting of eigenvectors of $$A\text{.}$$

4. If $$A$$ is diagonalizable, then $$A^{10}$$ is also diagonalizable.

5. If $$A$$ is diagonalizable, then $$A$$ is invertible.

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