- 14

- 1

My first idea was:

$$P_1=|u_1\rangle\langle u_1|, P_2=|u_2\rangle\langle u_2|$$

$$P_1P_2= |u_1\rangle\langle u_1|u_2\rangle\langle u_2|\neq 0$$

the second expression is not zero if ##\langle u_1|u_2\rangle## are not orthononal.

But I do not really get on with this task, which is why I hope for some advice.