Let (V,,) be an inner product space, and suppose that T : V V is a linear transformation. Recall that the norm of x V is x = px, x. (a) ShowthatifT(x),T(y)=x,yforallx,yV,thenT(x)=xforallxV. (b) ShowthatifT(x)=xforallxV,thenT(x),T(y)=x,yforallx,yV. (c) If we replace T with a function f : V V which is not necessarily linear, does (a) still hold? Does (b) still hold? If yes, explain why. If no, provide a counterexample