Q1: Consider the matrix $\begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}$. What are the eigenvalues?

A1: $-i$ and $i$

A2: $-1$ and $1$

A3: $-i$ and $1$

A4: $-1$ and $i$

Q2: Consider the matrix $ A = \begin{pmatrix} 0 & 1 \ -1 & 0 \end{pmatrix}$. What are the eigenvalues of the matrix $A^{10}$?

A1: Only $-1$

A2: $-1$ and $1$

A3: $-i$ and $1$

A4: Only $1$

A5: $0$ and $1$

Q3: Let $ A $ be a matrix with spectrum ${ 0, 1}$. Now consider the matrix $B = A^3 + 2 A^2 - 1$. What is correct?

A1: $\mathrm{spec}(B) = { -1, 2 } $

A2: $\mathrm{spec}(B) = { 0,1 } $

A3: $\mathrm{spec}(B) \subseteq { 0 } $

A4: $\mathrm{spec}(B) \supseteq { 0, 1} $