# Compute all Elements of a subgroup GL_3(R)

Hi there, i have two matrices A and B, they both out Gl_3(R). I have find all Elements in the Subgroup created by these two. is there a way to do it in sage?

M3 = MatrixSpace(QQ, 3) # Rational numbers print("Identity matrix:") show(M3.identity_matrix()) A = M3.matrix([[1, 0, 0], [0, -1, 0], [0, 0, -1]]) B = M3.matrix([[0, 1, 0], [0, 0, 1], [1, 0, 0]])

There should be 36 Elements in this group B is cyclic B^3=I and A creates 2 possible Element by negating elements. so the Left inverses create 6 Elements and the Right creates also 6, total is 36.