A real $2 \times 2 $ matrix $M$ such that $M^2 = \tiny \begin{pmatrix} -1&0 \\ 0&-1-\epsilon \\ \end{pmatrix}$ , then : 
A real $2 \times 2 $ matrix $M$ such that $$M^2 =  \begin{pmatrix} -1&0 \\ 0&-1-\epsilon  \\   \end{pmatrix}$$
(a) exists for all $\epsilon > 0$.
(b) does not exist for any $\epsilon > 0$.
(c) exists for some $\epsilon > 0$.
(d) None of the above is true.

Attempt: I couldn't think of any theory base to prove / disprove the existence of such a matrix.
Could someone please give me a hint on how to go about this problem?
Thank you very much for your help in this regard.

(I assume $M$ is supposed to be real; if it is allowed to be complex, then the exercise is trivial.)
Hint


*

*What are the possible eigenvalues of $M$?

*What can one say about the eigenvalues of real $2 \times 2$ matrices...?



Continued hint ...in particular what can one say about the eigenvalues of real $2 \times 2$ matrices when those eigenvalues are nonreal?

