# Unitary Matrices

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1. show that for a 2x2 unitary matrix its determinant is a complex number of unit modulus

2. Verify that the Pi/2 rotation matrix is orthogonal.

3. Verify that the matrices:

A= 1/sqrt(2) * ( 1 i )

( i 1)

and:

B = 1/2 * ( 1+i 1-i )

( 1-i 1+i )

are unitary. Verify that their determinant is of the form exp (i *theta)

Are they Hemitian?

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##### Solution Summary

The solution discusses the properties of unitary matrices.

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Let U be a unitary matrix and

Then its conjugate transpose is

Which means:

Where denotes complex conjugation.

And ...

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