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

A1: No other matrix can be equivalent 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 $A$, $B$ equivalent matrices. What is a correct implication?

A1: There are invertible matrices $S,T$ such that $ SA = B T$

A2: There is an invertible matrix $T$ such that $ A = T^{-1} B T$

A3: $AB$ is the zero matrix.

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

A5: $A,B$ are square matrices.

Q3: Are the matrices $A = \begin{pmatrix} 1 & 0 \ 0 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \ 2 & 2 \end{pmatrix}$ equivalent?

A1: Yes!

A2: No!

A4: One needs more information.