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Homework Statement
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)*
Homework Equations
As shown above.
<T(x),y> = <x,T*(y)>
The Attempt at a Solution
Well, I figure you only need to show that the equation holds, that shows that T* is invertible, since its inverse exists.
Now, I try to do something with the inner products:
<(T^-1)(x),y> = <x,(T^-1)*(y)>
I’m not sure how to “flip” inverse and the star.
Thanks for your help! =)