Question: Need help on a linear algebra homework problem where it requires to show that (.,.)_T is an inner product on V iff T is injective.

Need help on a linear algebra homework problem where it requires to show that (.,.)_T is an inner product on V iff T is injective. Thank you in advanced!

Suppose V is an inner product space, and let TE C(V). Define a function from V x V to F by setting (u, v)T = (Tu, Tv). Show that (, .)7 is an inner product on V if and only if T is injective

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