6. Let A and B be n x n hermitian matrices. Suppose that A² = Ins B² = In (1) and [A, B]+ = AB + BA=0n. (2) Let x € Cn be normalized, i.e. ||x|| = 1. Here x is considered as a column vector. (i) Show that (x* Ax)² + (x* Bx)² ≤ 1. (3) (ii) Give an example for the matrices A and B.

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A: Solution

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