Check: For each of the following permutations $\rho$ in $S(6)$ write $\rho$ as the product of transpositions For each of the following permutations $\rho$ in $S(6)$ write $\rho$ as the product of transpositions:


*

*$\begin{pmatrix} 1 & 3 & 5 & 4 & 6 & 2 \end{pmatrix}=\begin{pmatrix} 1 & 2 \end{pmatrix}\begin{pmatrix} 1 & 6 \end{pmatrix}\begin{pmatrix} 1 & 4 \end{pmatrix}\begin{pmatrix} 1 & 5 \end{pmatrix}\begin{pmatrix} 1 & 3 \end{pmatrix}$

*$\begin{pmatrix} 1 & 2 & 5 & 4 \end{pmatrix} \begin{pmatrix} 1 & 5 &
    3 & 6 & 2 \end{pmatrix}=\begin{pmatrix} 1 & 2
    \end{pmatrix}\begin{pmatrix} 2 & 5 \end{pmatrix}\begin{pmatrix} 5 &
    4 \end{pmatrix}\begin{pmatrix} 1 & 5 \end{pmatrix}\begin{pmatrix} 5
    & 3 \end{pmatrix}\begin{pmatrix} 3 & 6 \end{pmatrix}\begin{pmatrix}
    6 & 2 \end{pmatrix}$


Are these correct?

I'm assuming you're using the right-sided convention, in which case they are right.
