Hi, I am trying to prove the following equality

Range(T*T) = Range(T*)

where T is a linear transformation and * denotes the adjoint.

I know I must first show that Range(T*T) $\displaystyle \subset$ Range(T*) and vice versa.

so, Let w exist in R(T*T), then there exists a v in vector space V s.t.

T*T(v) = w.

Then I draw a blank, what's next??? Or am I even starting it correctly?

Thanks