I'llhelpyou with the problem. Note first that if for all (where [tex]V{/math] is our inner product space) then (indeed, take and subtract). From this we get that if for all then (indeed, note that ...conclude from the first part). Now, to our actual problem let and compute that our assumption gives . Pick cleverly (don't think too hard) to create a system of equations that will reduce this problem to the last one (note that you'll have to pick one of the values of to be non-real otherwise you'll have disproved the second part). For the second part take your inner product space to be with the usual inner product and recall that the inner product of orthogonal vectors is orthogonal...so what if a transformation sent a vector to its orthogonal vector.