{[3,3i],[-3i,3]}
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The matrix is normalized when its determinant is 1. This one has a determinant of 18, so each term needs to be divided by √18 = 3√2. One normalized version of this matrix is
.. {[1/√2, i/√2], [i/√2, 1/√2]}
.. {[1/√2, i/√2], [i/√2, 1/√2]}