Suppose that A E M(C). Prove that: (a) if A is unitary, then [det(A)] = 1....

 

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Suppose that A E M(C). Prove that: (a) if A is unitary, then [det(A)] = 1. (b) if A has real entries, then det(A) E R and hence if A is also unitary, then det(A) = 1 (c) if A M(R) is unitary and det(A) = +1, then A = a Fb] [ba] for some a, b E R with a + b = 1 Suppose that A E M(C). Prove that: (a) if A is unitary, then [det(A)] = 1. (b) if A has real entries, then det(A) E R and hence if A is also unitary, then det(A) = 1 (c) if A M(R) is unitary and det(A) = +1, then A = a Fb] [ba] for some a, b E R with a + b = 1