{"app":{"locale":"en-GB"},"problem":{"content":"

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).

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