Show that every self-adjoint operator on a finite-dimensional inner product space is normal. is the converse true? justify your answer. let v be an inner produc

Show that every self-adjoint operator on a finite-dimensional inner product space is normal. Is the converse true? Justify your answer. Let V be an inner product space over R and let T be a normal operator on V. Then show that T-3/ is normal, where I is the identity operator on V.