Q1: Which of the following matrices is similar to the zero matrix $\begin{pmatrix}0 & 0 \ 0&0 \end{pmatrix}$?

A1: No other matrix can be similar to the zero matrix.

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

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

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

Q2: Let $A$, $B$ similar matrices. What is a correct implication?

A1: $A$ and $B$ are equivalent matrices.

A2: $A-B$ is the identity matrix.

A3: $AB$ is the zero matrix.

A4: $A$ and $B$ are diagonal matrices.

Q3: Are the matrices $\begin{pmatrix} 1 & 0 \ 0 & 2 \end{pmatrix}$ and $\begin{pmatrix} 2 & 0 \ 0 & 1 \end{pmatrix}$ similar?

A1: Yes!

A2: No, they are not even equivalent.

A3: No, but they are equivalent because they have the same rank.

A4: One needs more information.