12. The operator x can be written in the matrix representation as x = = (5)...

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12. The operator x can be written in the matrix representation as x = = (5) a. Find the normalised eigenvectors of x with their corresponding eigenvalues. b. Show that eix (cos 0)1 + i(sin0)x, where 1 is the identity operator. Is this statement true for any 2x2 matrix, or does your proof invoke some more specific property of x? 12. The operator x can be written in the matrix representation as x = = (5) a. Find the normalised eigenvectors of x with their corresponding eigenvalues. b. Show that eix (cos 0)1 + i(sin0)x, where 1 is the identity operator. Is this statement true for any 2x2 matrix, or does your proof invoke some more specific property of x?