# Math Help - conjuacy class

1. ## conjuacy class

Need some help on the following:

If we let [x] be conjugacy class of x in group H. Show that $\mid\left [ h\right ] \mid = \mid\left[ h^{-1} \right ] \mid$ for any element h in H

Thank you for help

2. Let $G$ be group. To show that $| [h] | = | [h^{-1}]|$ you need to show there is a one-to-one correspondence $\phi: [h]\mapsto [h^{-1}]$. Let $x\in [h]$ then it means $x=ghg^{-1}$ for some $g\in G$. Define $\phi(x) = g x^{-1} g^{-1}$. Show this mapping is well-defined. Now show it is a bijection.