##### Exercise3

Suppose that $$A$$ is an $$n\times n$$ matrix.

1. Suppose that $$A^2 = AA$$ is invertible with inverse $$B\text{.}$$ This means that $$BA^2 = BAA = I\text{.}$$ Explain why $$A$$ must be invertible with inverse $$BA\text{.}$$

2. Suppose that $$A^{100}$$ is invertible with inverse $$B\text{.}$$ Explain why $$A$$ is invertible. What is $$A^{-1}$$ in terms of $$A$$ and $$B\text{?}$$

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