Q1: Do the following to matrices have the same determinant? $$A = \left( \begin{array}{cccc}1 & 0 & 3 & 0 \ 0 & 3 & 1 & 0 \ 2 & 0 & 1 & 2 \ 5 & 0 & 1 & 1 \\end{array} \right) $$ $$B = \left( \begin{array}{cccc}1 & 1 & 3 & 0 \ 0 & 3 & 1 & 0 \ 2 & 2 & 1 & 2 \ 5 & 5 & 1 & 1 \\end{array} \right) $$

A1: Yes!

A2: No!

A3: One needs more information.

Q2: Assume $A \in \mathbb{R}^{4 \times 4}$ has determinant $3$ and $B = 2\cdot A$. What is the determinant of $B$?

A1: $48$

A2: $16$

A3: $3$

A4: $4$

A5: $12$

A6: One needs more information.