Q1: The matrix $$ \begin{pmatrix} 0 & \sqrt{2} & 1 \ 1 & \sqrt{3} & 0 \end{pmatrix}$$ is an element of which set?

A1: $ \mathbb{R}^{2 \times 3}$

A2: $ \mathbb{R}^{1 \times 3}$

A3: $ \mathbb{R}^{3 \times 2}$

A4: $ \mathbb{R}^{2 \times 2}$

Q2: What is the neutral element with respect to the addition in $\mathbb{R}^{3 \times 2}$?

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

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

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

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

Q3: Is the equation $$ 2 \cdot \begin{pmatrix} 1 & 2 \ 2 & 4 \end{pmatrix} = \begin{pmatrix} 1 & 2 \ 2 & 4 \end{pmatrix} + \begin{pmatrix} 1 & 2 \ 2 & 4 \end{pmatrix}$$ correct?

A1: Yes!

A2: No!