# Thread: help with adjoints of linear operators!

1. ## help with adjoints of linear operators!

I need help with the following proof:
Let V be a finite=dimensional inner product space and let T be a linear operator on V. Prove that if T is invertible, then T* is invertible and (T*)^-1 =(T^-1)*.
Thanks for any suggestions and help!

2. Originally Posted by dannyboycurtis
I need help with the following proof:
Let V be a finite=dimensional inner product space and let T be a linear operator on V. Prove that if T is invertible, then T* is invertible and (T*)^-1 =(T^-1)*.
Thanks for any suggestions and help!

$\forall x\in V\, ===$ $\,\Longrightarrow\,=0\,\Longrightarrow\,T^{*}\left(T^{-1}\right)^{*}-I=0$ ...

Tonio

3. Originally Posted by dannyboycurtis
I need help with the following proof:
Let V be a finite=dimensional inner product space and let T be a linear operator on V. Prove that if T is invertible, then T* is invertible and (T*)^-1 =(T^-1)*.
Thanks for any suggestions and help!
$===,$ for all $x,y \in V,$ and so $(T^{-1})^*T^*=\text{id}_V.$