(i) Let A be an n x n matrix over C and II be an m x m projection matrix. Let z E C. Calculate exp(z(A > II)). (ii) Let A₁, A2 be n x n matrices over C. Let II₁, I2 be m x m projection matrices with II₁I₂ = On. Calculate exp(z(A₁II₁ + A₂ II₂)). (iii) Use the result from (ii) to find the unitary matrix U(t) = exp(-iĤt/ħ) where Ĥ = ħw(A₁II₁ + A₂II₂) and we assume that A₁ and A2 are hermitian matrices.

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