2. In a three-dimensional vector space, consider the operator whose matrix in an orthornormal basis (1),...

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2. In a three-dimensional vector space, consider the operator whose matrix in an orthornormal basis (1), 2), 3)} is 0 0 A=0 -1 0 1 0 0 19 (a) Show that A Hermitian. (2) (b) Calculate its eigenvalues and find the orthonormal eigenvectors corresponding to them. (10) (c) Calculate the matrices representing the projection operators for each of the eigenvectors found in part (b). (8) [201 2. In a three-dimensional vector space, consider the operator whose matrix in an orthornormal basis (1), 2), 3)} is 0 0 A=0 -1 0 1 0 0 19 (a) Show that A Hermitian. (2) (b) Calculate its eigenvalues and find the orthonormal eigenvectors corresponding to them. (10) (c) Calculate the matrices representing the projection operators for each of the eigenvectors found in part (b). (8) [201