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

Let \A be the incidence matrix of lines and points of the classical projective 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 these submatices over \Ff_q, the defining field of $PG(2,q)$, is determined