Compute Inversion of (143) Cycle

[rayman123]

Homework Statement

Find an inversion of the following cycle
(143)

Homework Equations

(143)^{-1}

The Attempt at a Solution

Could someone show me how do we compute this?

 

[tiny-tim]

hi rayman123!

just go back to the definition of (143) …

what does (143) do to 1?
what does (143) do to 3?
what does (143) do to 4?

now what would its inversion do to 1, to 3, and to 4?

 

[rayman123]

hi rayman123!

just go back to the definition of (143) …

what does (143) do to 1?
what does (143) do to 3?
what does (143) do to 4?

I guess 1 is being moved to 4
4 goes to 3
and 3 goes to 1

now what would its inversion do to 1, to 3, and to 4?

I do not know...:(

I know how to find an inversion for something like that for example
\left( {\begin{array}{cc}<br /> 123 \\<br /> 231 \\<br /> \end{array} } \right)^{-1}=\left( {\begin{array}{cc}<br /> 231 \\<br /> 123 \\<br /> \end{array} } \right)=\left( {\begin{array}{cc}<br /> 123 \\<br /> 312 \\<br /> \end{array} } \right)

 

[tiny-tim]

ok, then write (143) in that two-row form, and then invert it