$3]$ The Fredkin gate is another universal gate in classical computing, defined as follours:

$,$ where

$|y^{\text{'}}$:

In other words, the $|y$: bits are swapped iff $|x$: i$]$ Write out the matrix corresponding to the Fredkin gate. ii$]$ What values for $|y$: yield $|x$: as one of the outputs for any $|x$: $?$