Q1: Let $A,B$ be matrices given by $A = \begin{pmatrix} 1 & 2 & 3 \ 0 & 1 & 2 \end{pmatrix} $ and $B = \begin{pmatrix} 1 & 2 \ 1 & 2 \end{pmatrix}$. Which claim is correct?

A1: The matrix product $B A$ is well-defined.

A2: The matrix product $A B$ is well-defined.

A3: The matrix product $A A$ is well-defined.

A4: The matrix product $B B$ is equal to $A$.

Q2: Let $A,B$ be matrices given by $A = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 2 & 3 \ 0 & 1 & 2 \end{pmatrix} $. What is the matrix product $AB$?

A1: $B$

A2: $A$

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

A4: $\begin{pmatrix} 1 & 2 & 2 \ 2 & 1 & 2 \end{pmatrix} $

A5: $0$

Q3: Let $A,B$ be matrices given by $A = \begin{pmatrix} 1 & -1 \ -1 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 2 \ 0 & 1 \end{pmatrix} $ and . What is the matrix product $AB$?

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

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

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

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