Ponderable 3.2.1

(a) Clic on the image to open the odg file.

The inverse of the permutation can be read backwards, and ${\left(\begin{array}{ccc}1& 2& 3\\ 2& 1& 3\end{array}\right)}^{\mathrm{-1}}=\left(\begin{array}{ccc}1& 2& 3\\ 2& 1& 3\end{array}\right)$. It’s itself.

(b)

Backwards, we get: ${\left(\begin{array}{cccc}1& 2& 3& 4\\ 2& 3& 4& 1\end{array}\right)}^{\mathrm{-1}}=\left(\begin{array}{cccc}1& 2& 3& 4\\ 4& 1& 2& 3\end{array}\right)$.

(c)

Backwards: ${\left(\begin{array}{ccccc}1& 2& 3& 4& 5\\ 2& 1& 5& 3& 4\end{array}\right)}^{\mathrm{-1}}=\left(\begin{array}{ccccc}1& 2& 3& 4& 5\\ 2& 1& 4& 5& 3\end{array}\right)$.

Maison