= Solution
Using the printed $x,y$ axes, take a lower vertex of cell B as origin. One allowed pair of <primitive lattice translation vectors> is
$$
\boxed{\mathbf a_1=a(\hat{\mathbf x}+\hat{\mathbf y}),\qquad
\mathbf a_2=a(-\hat{\mathbf x}+\hat{\mathbf y})}.
$$
Both vectors connect nearest <lattice points>, have length $\sqrt2a$, and are perpendicular. Their determinant has magnitude $2a^2$, consistent with a primitive area. Exchanging them or reversing their directions gives equivalent basis conventions; the corresponding <reciprocal lattice vectors> must then use the same convention.
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