Permutations and cycles

Question

Apologies for the image but I dont know how to mathjax the content in the picture

I was just hoping for confirmation of my answers since I feel im wrong for some reason

a) I got (12345678)/(74823561)

b) sigma=(146)(2837)

c) (12345678) / (36581247)enter image description here

Answer 1

I do agree for all your answers (a),(b),(c)

(c), I think that you forgot one question, it is also asked to write $\tau^{-1}$ in standard cycle form,

I find:

$$ \tau^{-1}=(1,3,5)(2,6)(4,8,7) $$

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Maybe you can learn how to write equations in $\LaTeX$, one tutorial here

Example of my answer:

$$
\tau^{-1}=(1,3,5)(2,6)(4,8,7)
$$