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I need to show the following equalities, where T is a linear transformation and * is the adjoint.

Null(T*T) = Null(T)

Range(T*T) = Range(T)

The attempt at a solution

I know I have to show that Null(T) is a subset of Null(T*T) and then Null(T*T) is a subset of Null T....

Letvexist in Nullspace of T. Then T(v) = 0

Now letvexist in the Nullspace of T*T. Then T*T(v) = 0

Now i am lost, any help would be great. Thanks

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# Linear Transformation Equalities

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