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Let $\A$ be the incidence matrix of lines and points of the classicalprojective plane $PG(2,q)$ with $q$ odd. With respect to a conic in $PG(2,q)$,the matrix $\A$ is partitioned into 9 submatrices. The rank of each of thesesubmatices over $\Ff_q$, the defining field of $PG(2,q)$, is determined.

Some $p$-ranks related to a conic in $PG(2,q)$