Let T be an orthogonal [unitary] operator on a finite-dimensional real [complex] inner product space V. If W is a T-invariant subspace of V, prove the following results. (a) TW is an orthogonal [unitary] operator on W. (b) W⊥is a T-invariant subspace of V. Hint: Use the fact that TW is one-to-one and onto to conclude that, for any y ∈W, T∗(y) =T−1(y) ∈W. (c) TW⊥ is an orthogonal [unitary] operator on W.

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