Hi, I have this question and I'm not sure if i'm going about it in the right way.

Let , are permutations.

Prove that sgn( ) = sgn( )

I know that permutations can be written as a product of transpositions. So is this right?

where are transpositions. (I'm not sure if the inverse of does have the same number of transpositions as ?)

Then sgn( ) =

sgn( ) =

sgn( ) =

So sgn( ) = = sgn( )

Is this right?

Any help would be appreciated,

Thanks,

Katy