Some matrix completions over integral domains

We characterize 3×33×3 nilpotent matrices which are completions of 2×22×2 arbitrary matrices and 3×33×3 idempotent matrices which are completions of 2×22×2 arbitrary matrices over integral domains. As an application we show that a nil-clean element of a ring which belongs to a corner of the ring, may not be nil-clean in this corner.