Q1: What is the correct rule of Sarrus for the matrix $$ \begin{pmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \ \end{pmatrix} $$ with real entries?

A1: $$a_{11} a_{22} a_{33} + a_{21} a_{32} a_{13}+ a_{31} a_{12} a_{23} - a_{13} a_{22} a_{31} - a_{23} a_{32} a_{11}- a_{33} a_{12} a_{21} $$

A2: $$a_{11} a_{22} a_{33} + a_{21} a_{32} a_{13}+ a_{31} a_{12} a_{23} - a_{13} a_{22} a_{31} + a_{23} a_{32} a_{11}+ a_{33} a_{12} a_{21} $$

A3: $$a_{11} a_{22} a_{33} + a_{21} a_{32} a_{13}- a_{31} a_{12} a_{23} - a_{13} a_{22} a_{31} + a_{23} a_{32} a_{11}+ a_{33} a_{12} a_{21} $$

Q2: Calculate the determinant of the matrix $$ \begin{pmatrix} 2 & 3 & 4 \ 0 & 1 & 3 \ 0 & 0 & 3 \ \end{pmatrix} $$

A1: $6$

A2: $2$

A3: $-3$

A4: $1$

Q3: Calculate the determinant of the matrix $$ \begin{pmatrix} 2 & 1 & 4 \ 1 & 1 & 3 \ 1 & 2 & 3 \ \end{pmatrix} $$

A1: $-2$

A2: $6$

A3: $-3$

A4: $1$