Consider the matrix M = 3 -1
Verify that M^2= 2M -I
the question is what is I ??
It's the integer equivalent of 1 under multiplication.
ie. if A is an integer A*1 = A.
For 2x2 matrices the identity has
[ 1 0 ]
[ 0 1 ]
for 3x3s it's
[1 0 0 ]
[0 1 0 ]
[0 0 1 ]
And so forth. I don't know how to draw matrices in this thing... sorry...
Side note: has been got using the Cayley-Theorem Theorem: Cayley-Hamilton Theorem
Edit: Whoops, I just realised that your question wasn't find the inverse of M. Not to worry, since you asked what I is I figure I've probably anticipated what your next question is.