# Worked Problems in Physics

## Nielsen and Chuang Exercise 2.32

Posted in Nielsen/Chuang by rpmuller on March 7, 2010

Exercise 2.32 Show that ${A\otimes B}$ is a projector if ${A,B}$ are projectors.

We want to show that ${P^2=P}$ here:

$\displaystyle (A\otimes B)^2 = A^2\otimes B^2 = A\otimes B$

Hence ${A\otimes B}$ is a projector if ${A,B}$ are.