# Problem 572: Idempotent matrices
A matrix \$M\$ is called idempotent if \$M\^2 = M\$. Let \$M\$ be a
three by three matrix : \$M=\\begin{pmatrix} a & b & c\\\\ d & e & f\\\\
g &h &i\\\\ \\end{pmatrix}\$. Let C(n) be the number of idempotent three
by three matrices \$M\$ with integer elements such that \$ -n \\le
a,b,c,d,e,f,g,h,i \\le n\$. C(1)=164 and C(2)=848. Find C(200).