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Basically, I was wondering how to prove the following statement. Ive seen it in the Hamermesh textbook without proof, so I wanted to know how you go about doing it.

Let's say you have a group element [itex]g_{1}[/itex], which has a corresponding inverse [itex]g_{1}^{-1}[/itex]. Let's also define a linear transformation D for this group element.

So what im trying to prove is that

[itex]D(g_{1}^{-1}) = [D(g_{1})]^{-1} [/itex]

Can u guys point me in the right direction?

Thanks!