ISI2015-MMA-38

Question

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

• A. exists for all $\varepsilon > 0$
• B. does not exist for any $\varepsilon > 0$
• C. exists for some $\varepsilon > 0$
• D. none of the above is true

Comments

Option B is the correct answer.