Q1: Which matrix $A \in \mathbb{C}^{2 \times 2}$ is similar to the identity matrix?

A1: $$ \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} $$

A2: $$ \begin{pmatrix} 1 & 0 \ 0 & -1 \end{pmatrix} $$

A3: $$ \begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix} $$

A4: $$ \begin{pmatrix} 0 & 1 \ 1 & 0 \end{pmatrix} $$

A5: $$ \begin{pmatrix} -1 & 0 \ 0 & -1 \end{pmatrix} $$