Hey all, this is one of my practice questions and I have no idea where to start.

Find a 5 by 5 permutation matrix P which has 1 in its (5,4)-place and so that the smallest power of P which gives the identity matrix is P6 .

(Hint: Consider "combining" a 2 by 2 permutation matrix with a 3 by 3 one.)

There are several correct different solutions.

The question has been designed so that there should be a block diagonal permutation matrix solution.

I haven't actually encountered permutation matrices before, but I've looked up the basics (what they do, how to apply them).