general linear group finite field
I am trying to compute the number of 3 x 3 matrices A over the field of p elements (p prime) such that A^2 = I. I wrote the following code which gives me the answers for p=2 and p=3, but it is taking for ever to compute when for p=5. Is there a better way to do this job which can speed up the computations? Many thanks for help.
def num_invol(n): G = GL(n,GF(3)); sum = 0 for A in G: if A^2 == G.one(): sum = sum +1 return sum for p in (2..11): if p.is_prime(): print (p, num_invol(p))