Quantum Country exercise 6

This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for convenience in referring to them.

Exercise 6. Show that the identity matrix I is unitary.

Answer: Since I is symmetric we have I^T = I and since the values of I are all real we have \left( I^T \right)^* = I^T. We thus have I^\dagger I = \left( I^T \right)^* I = I^T I = II = I by the definition of I.

Since I^\dagger I = I the matrix I is unitary.

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