## normal orthogonality problem

1)A)T is a normal in V inner product space
there is $M_{1}(t),M_{2}(t)$ different polinomial $u,v\in V$
prove that if $M_{1}(T)u=0$ and $M_{2}(T)v=0$ then u orthogonal to v?
how i tried:
i have defined $Q_{1}$ and $Q_{2}$and proved that v is eigen vector of $M_{2}(t)Q_{2}(t)$ of eigenvalue 0.
and u is eigen vector of $M_{2}(t)Q_{2}(t)$ of eigenvalue 1.
so if $M_{2}(t)Q_{2}(t)$ is normal then u is orthogonal to v.
but how to prove that M_{2}(t)Q_{2}(t) is normal?
i cant show here that TT*=T*T

MQ(MQ)*=MQQ*M*
(MQ)*MQ=Q*M*MQ
those two are not the same
??