unitary,close to it self defintion question

there is A matrices order n over C.we define a transformation T as T(B)=AB for every B

A.prove that if A unitary if and only if T is unitary ?

B.prove that if A normal if and only if T is normal ?

C.prove that if A close to itselfs if and only if T is close to itself ( )?

i wrote the definition near each question ,also i know this .

for A.

what next?

the prof uses (T(x1),x2)=(x1, (x1))

i dont know this definition and how it linked to the transformation we are asked to do

?