Quantum Country exercise 6

Posted on October 13, 2021 by hecker

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 $I$ .