ok, this is what i have, but you may want to check my arithmetic, because i DO make mistakes:

the Cayley-Hamilton theorem tells us M satisfies its own characteristic equation, which is .

therefore: , or put another way:

.

the trouble is now how to express in terms of . to accomplish that, we write:

, so that evidently:

, or:

, and re-arranging:

.

substituting back in our original equation:

, obtaining:

p = 23, q = -18, r = -40.