You should then figure out what degrees of freedom each element contain, Which can be accessed via
dolfinx.fem.FunctionSpace.dofmap.cell_dofs(cell_index) this will give you want degrees of freedom (not unrolled with the block size of the problem, 3 for 3D elasticity) are in the cell. You can then use this to extract the rows and columns of the matrix, by either converting the PETSc mat to a dense matrix, or a csr matrix.