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A real $2 \times 2$ matrix $M$ such that $$M^2 = \begin{pmatrix} -1 & 0 \\ 0 & -1- \varepsilon \end{pmatrix}$$

1. exists for all $\varepsilon > 0$
2. does not exist for any $\varepsilon > 0$
3. exists for some $\varepsilon > 0$
4. none of the above is true

1
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