When can a real nxn matrix have (-I) as its d-th power?

[astonmartin]

Homework Statement

For what positive integers x and n is there a real nxn matrix whose d-th power is -I (negative identity matrix)

Homework Equations

The Attempt at a Solution

I don't really understand this problem, aren't there endless possibilities? Also, why does it matter what size the matrix is?

 

[Dick]

What's this mysterious integer x? Is it the same as d?

 

[astonmartin]

Yeah sorry that's supposed to be a d. I'm assuming there is a solution to this other than the negative identity matrix?

 

[Dick]

Well, yes, e.g. A=[[0,1],[-1,0]] is a 2x2 matrix and A^2=-I.