Answer
See below
Work Step by Step
Let $E_{in}$ be an elementary $n \times n$ matrix obtained by permuting two rows of the identity matrix $I_n$.
By $P_1$ then gives us $\det(E_{in}) = -\det(I_n)=-1$.
Let $E_{2n}$ and the elementary $n \times n$ matrix be obtained from the identity matrix $I_n$ by multiplying one row by the number of rows in the matrix. By P3 then gives us $\det(E_{3n}) = \det(I_n) = 1$.
Let $E_{3n}$ be an elementary $n \times n$ matrix obtained by scaling a row by $k$ from the identity matrix $I_n$. By P2 then gives us $\det(E_{3n}) = kdet(I_n) = k.$
The formula for $\det(E)$ given in the text at the beginning of the proof of P9 is derived from the above results.
